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1. Edges visible arrows 13D _ Color interpolation _ Size interpolation Others Orthogonal projection Background color This dialog is diaplayed when clicking on the Dialogs gt Rendering Parameters Ctrl R lenables to configure the rendering of the graph The available options are grouped in the following three frames e Labels the options in this frame only affect the display of the labels eVisibility you can enable disable the display of labels on nodes edges or metanodes e Type this indicates the text display mode which can be one of Bitmap Texture or 3D emetric ordering when checked the labels are displayed in using the viewMetric property decreasing order e Density use this slider to avoid having too much labels displayed max is on the left e Edges this frame options affect the way the edges are displayed visible enables disables the display of edges If not checked the other options of this frame are not active e arrows enables disables the display of arrows e 3D enables disables the display of edges in 3D eColor interpolation when checked the edge color is interpolated from the color of its source node to the color of its target node eSize interpolation when checked the edge size is interpolated from the size of its source node to the size of its target node e Others the options in this frame are related to general aspects of the rendering eOrthogona
2. e Add Add the nodes or edges to be selected to the current selection e Remove Remove nodes or edges from the current selection e Intersect Select the intersection between the nodes or edges TO BE selected and the ones from the current selection eAlgorithm this one is divided in several parts to make a difference between the kind of algorithms you can apply These are e Selection this submenu is populated by selection algorithms These algorithms allows to select nodes and or edges assign the viewSelection property see Section 3 3 Properties of graph for more details satifying some criteria For example the Loop Selection algorithm detects all edges for which the starting and ending nodes are the same eColor this submenu is populated by color algorithms These king of algorithm computes the color the viewColor property see Section 3 3 Properties of graph for more details of the graph elements A default one Metric Mapping is provided it allows to color all graph elements according to a metric property e Measure this submenu is populated by metric algorithms These algorithms allows to compute and assigned a value to the viewMetric property of graph elements see Section 3 3 Properties of graph for more details For example when running the Degree algorithm the degree the number of its neighbors is compute and assigned to each graph node view
3. This selection algorithm can be used to select a sub graph without any cycle Algorithm documentation 3 2 1 7 Spanning Forest This algorithm can be used to create a set of spanning trees out of the graph A tree is a special kind of graph that has the following properties e Has a root a starting point node e A node have severals sons and their is only one edges targeting each sons e Doesn t have any cycle e A leaf is an ending node E RA doxy gen allPlugins html ReachableSubGraphSelection R L doxygen allPlugins html SpanningDagSelection 21 Func tion al 1 ties Algorithm documentation 3 2 2 Color Algorithms 3 2 2 1 Metric Mapping The metric mapping algorithm can be used to re color the nodes of the graph after using a measure Section 3 2 3 Measure algorithm This Algorithm takes 5 parameters eProperty Property is a metric value It is used to affect scalar values to graph items eColormodel Color can be either 1 or 0 1 for RGB interpolation and O for HSV interpolation e Type If type is checked the color mapping will be uniform which means that if you have 2 nodes with the property value equals to O there will be 2 nodes colored in colorl If type is not checked the color quantification will be linear which means that if you have 2 nodes with the property value equals to 0 there will be 1 node colored in colorl and an other with a lighter colorl eColorl
4. e orientation vertical horizontal e orthogonal enables the drawing of the edges orthogonally bent e layer spacing space between the levels of the Tree e node spacing space between nodes sibling nodes e bounding circle 1f checked the estimation of overlapping nodes will be computed with bounding circles instead of bounding rectangles Algorithm documentation gt 3 2 4 2 5 Improved Walker The improved walker layout is just a hierarchical layout Algorithm documentation 3 2 4 2 6 Squarified Tree Map The squarified tree map layout will place nodes in nested rectangles For example lets take a tree with a root and two sons the layout will draw a rectangle for the root containing two other rectangles 1ts sons This layout can be very useful for analyzing disks usages Here is an example Following is the tree a a file system containing 6 file of 1Mb and severals directories Sl doxygen allPlugins html Dendrogram 32 1 1 doxygen allPlugins html TreeReingoldAndTilfordExtended 33 J doxygen allPlugins html Improved Walker 38 Func tion al 1 _ties unnarmed_1 mal 14 11 2 10 1 3 1 1 4 1 1 3 2 l The same graph with a squarified tree map layout Using the 3D we can see how the layout is done 39 Func tion al 17 ties Algorithm documentation 3 2 4 2 7 Tree Leaf This layout looks like the improved walker but does not pack the nodes The result is a nice hie
5. applying the Algorithm gt Selection gt Reachable Sub Graph algorithm with distance 1 Create a new Subgraph Following is a hierarchical layout of the neighborhood of all outgoing edges one hop away that is the publications and coauthors of the union of Card and Robertson You can repeat those operations for Robertson only and Card only U O ri als The similarity of these final three images shows the very strong ties between these two authors You can now close this graph since we are going to use an other one for the following of this tutorial The next graph is similar to the old one but has links between author and conference by following links from author to paper and from paper to conference Then delete papers You can download it and open it in tulip 4 3 2 2 Central Authors and Conferences Overview To show the large scale structure of this dataset we colored Authors in green and conferences in blue with a GEM layout Algorithm gt Layout gt Force Directed gt GEM We deleted all the papers nodes By zooming in 6 http tulip labri fr samples ConfAuth tlp gz 67 U O ri als We select only the large connected component the big set of nodes Select a fiew nodes in the center of the component and run the Reachable Subgraph selection algorithm with distance set to 50 Color the authors by the Strahler metric Run the Algorithm gt Measure gt Graph gt Strahler algorithm andthenaAlgo
6. Paris Which means that Berlin and Paris are two articulation points of our graph Algorithm documentation 3 2 3 2 2 Connected Component A connected component is a maximal connected subgraph Two nodes are in the same connected component 1f and only if there exists a path between them After running the algorithm the index of the connected component of a node is saved in its viewMetric property It is the same for the edges For more details please visit Wikipedia Connected Component Algorithm documentation 3 2 3 2 3 Connected Tree Component The connected tree component algorithm can be useful to find parts of a graph that are trees Here is an example Following is a graph with on the left side a tree This graph forms a unique connected component l6 y doxygen allPlugins html BiconnectedComponnent 17 http en wikipedia org wiki Connected_component_ graph_theory 18 7 doxygen allPlugins html ConnectedComponent 28 Func tion al 17 thes As you can see the algorithm divided the graph into 2 components Algorithm documentation 3 2 3 2 4 Strongly Connected Component A directed graph is said to be strongly connected if for every pair of nodes Sl and S2 it exists two edges el and e2 such as e The Source of el is Sl and Target is S2 e The Source of e2 is S2 and Target is Sl 19 7 arxvoen allPlno doxygen allPlugins html ConnectedAndTreeComponent 29 Func tion al 1 t
7. Wikipedia Simple graphs eMake Acyclic A graph is acyclic if it contains no cycle A cycle is a path that as the same source and target For more information please visit Wikipedia Acyclic graphs eMake Connected A graph is said to be connected if every pair of vertices in the graph is connected For more information please visit Wikipedia Connectivity Make Bi connected For more information please visit Wikipedia Biconnected Graphs 1 eMake directed If the graph is a free tree make it directed If a node and only one node is selected this one will be considered as the root node If none is selected Tulip will heuristically choose the center of the graph as the root node For more information please visit Wikipedia Directed Tree e Reverse selected edges Exchange source and target of an edge View this is composed of the operations about a view It is possible to redraw center the current view create a new 3D view initially a copy of the current one Section 2 7 New 3D View eDialogs this menu allows to redisplay each of the dialog windows such as the info editor window or the 3D overview e Windows this menu contains two options for the management of the views in the workspace cascade or tile mode e Options this menu allows to enable disable the display options e Force ratio Tries to keep a good Height Width ratio for the layout of the graph e Map metric Applies the Color Metric Mappi
8. come back to the oldest view Select View gt Center view from the menu bar e Select Algorithm gt Measure gt Misc gt 1d from the menu bar to compute a value metric for each node and edge of the graph The graph is now displayed with colors depending of the metric You can change the colors with the menu Algorithm gt Color gt Metric Mapping This plugin computes an interpolation between the two selected colors 4 1 1 2 Creation of a graph In this section we learn how to create 1ts own graph element by element e Select the File gt New from the menu bar to create a new graph e Create a graph adding nodes and edges For a node select the mouse toolbar operation and click on the position you have chosen To insert an edge select the mouse toolbar operation Click on the source node then on the target node You can display or hide them with Edges checkbox in the Overview subwindow In the same way you can display or hide the arrows checking Arrows e Delete elements of the graph Select the OK mouse toolbar operation then click on the element you want to delete qu rl als 4 1 2 Save options To save your work you just have to select File gt Save or Save as a dialog appears allowing to enter the author of the graph and some comments then after clicking on the OK button just type the file name and choose its location The second way to make a save is to export the graph in a special format
9. element node or edge named metric the colors An other advantage of Tulip is that it is easy to add a new algorithm in the structure this way 1t 1s able to include lot of algorithms As explain in the Section 2 1 Main window Menus the algorithms are accessed by the Algorithms menu Several categories are in there Selection Color Layout Measure Size General They modify the properties of the graph elements 3 2 1 Selection Algorithms 3 2 1 1 Induced Sub Graph The induced Sub Graph algorithm can be used to obtain the edges that are between selected nodes Here is an example Before After Func tion al 1 ties Algorithm documentation 3 2 1 2 Kruskal The Algorithm of Kruskal is used to create a minimum spanning tree out of a connected graph It is divided in several steps e Make a list of the edges starting with the shortest one ending with the longest one e Add all edges with their from to nodes to the tree as long as you don t have any cycle Let s take an example We have a set of airports Bordeaux Paris L A the nodes and a set of Airports connections the edges As you can see this makes a very complicated Graph As edges do not all have the same weight in terms of price distance some of them are not really important the ones with a high weight The algorithm of kruskal will select the ones that we can t remove 2d doxygen allPlugins html InducedSu
10. layout It has a pretty bad angular resolution Indeed we do not see the leaves but only a large black rectangle of edges i Here is the same tree with a Bubble Tree layout The angular resolution is much better Func tion al 1 _ties Sr l Ae L 4 K a ER t Ja 1 N A Algorithm documentation 3 2 4 2 2 Cone Tree The cone tree 1s a 3d layout which seen from the top looks like a bubble tree It takes two parameters e node size e Orientation Vertical Horizontal Here 1s an example of this layout On the left side you can see a tree with a hierarchical classic layout and on zu le un ia S ir x e ba 2 ne e is F the right side the same tree but with a cone tree layout 29 Ja doxygen allPlugins html BubbleTree 36 ER ae SE Ir size of the node will depend of the metric that you choose The Algorithm will consider that parameter so that no nodes overlap themselves This can be useful if you want a node to be far from the others just take a new size Metric and give a higher value to that specific node Func ton al 1 _ties unnamed 1 win unnamed_1 unnamed 1 a Algorithm documentation 3 2 4 2 3 Dendrogram The dendrogram layout is a hierarchical layout on which every leaves are displayed on the same layer A dendrogram is a tree diagram frequently used to illustrate the arrangement of the clusters produced by
11. on an element of a graph node or edge Tulip displays all available properties of that node edge using the Element tab of the Info Editor sub window see Section 2 5 Info Editor Rectangle Selection Allows multiple elements selection Elements within the selection box are selected If Shift key is pressed the newly selected elements are added to the current selection if Ctrl key Alt key on Mac 1s pressed the selected elements are removed from the current selection else they replace the current selection Selection edition This tool allows to modify the current selection Available operations are horizontal stretch vertical stretch all axis stretch coordinate axis rotation and translation If no key is pressed coordinates are modified If Shift key is pressed only coordinates are modified If Ctrl is pressed only size is modified A left button click outside the selection box reset the selection Press on this circle to rotate the selection y Press on this triangle to change width or height of the selection e The square is used both for resizing AND rotating the selection P Magic Selection it enables to select all the graph connected nodes having the same metric It works like the magic selection in image editing software The difference is the topology of the graph Graphic er _ace Zoom Box It enables to zoom on a defined rectangle area The first corner of the rectangle i
12. the algorithm to give an indication on the number of nested cycles for graphs and at last All that will ask the algorithm to use both registers and stack For more information please visit http en wikipedia org wiki Strahler_Stream_Order Algorithm documentation 3 2 3 1 6 Strength Graph must be simple no loops This algorithm will compute the strength of edges Every edges with small values are important in the way that their removal can disconnect two connected components Every edges with a high value metric may belong to a strongly connected component Algorithm documentation gt 3 2 3 2 Component 3 2 3 2 1 Biconnected Component A connected graph is biconnected if the removal of any single node and his edges can not disconnect the graph The biconnected components of a graph are the maximal subsets of nodes such that the removal of a node from a particular component will not disconnect the component Note that unlike connected components a node can belong to multiple biconnected components For example we can use this algorithm on an airlines graph Such as the one following CE a doxygen allPlugins html StrahlerMetric IS 1 doxygen allPlugins html StrengthMetric 2d Func tion al 1 _ties The result is 3 biconnected components e Paris New York L A Madrid e Paris Berlin Berlin Moscow Prague The intersection of those 3 biconnected components is Berlin and
13. v3 0 0 0 Figure 2 3 ClusteringTab Graphic n er _face O Display Clustering Plane Compute Results 2 6 View window home bardet graph tlp The 3D graph view subwindow is the window where the graph is displayed It can display graph in two or three dimensions and enables to apply the mouse operations selected in the tool bar by directly clicking on the drawing of the graph If the user lets the mouse during few seconds on a node edge a tooltip window displays its id and label use Options menu to enable tooltips 2 6 1 Pop up menu of graph view node 1987 Add to Remove from selection Select Delete Go inside Ungroup Properties This pop up menu is displayed when pressing on the mouse right button press Ctrl key when mouse pressing on Mac while on a graph element and allows to perform simple actions on this element eAdd to Remove from selection this allows to change the selection state of the element 14 e Select the current element replaces the whole selection e Delete this permanently removes the element from the current graph eGo inside if the element is a metanode this shows the corresponding subgraph in the current view e Ungroup if the element is a metanode this permanently removes it and its corresponding subgraph eProperties this shows the element properties in the Element tab 2
14. will only depend of the numbers of metrics you add to the list With only one metric added you will have an frequency histogram displayed With two resp three metrics you will have a 2D resp 3D scatter plot Each metric representing a different dimension In the example we have only added the DAGLevel metric to the Used Metrics list Figure 4 3 A single metric for an histogram 11 u Tl als Auto Shape Conversion Cube Metrics Available Meincs Used Metrics Discretization Step x 1 Discretization Step y Discretization Step z Change to Histogram As you can see adding a metric implies some changes in the interface The bottom button becomes enabled so as the edit box corresponding to Discretization Step 1 You can specify a discretization step even if it is not really useful for our example Now the last step before having a beautiful frequency histogram displayed asking the panel to compute it Just click on the Compute Histogram button That s it You have your first histogram congratulations Figure 4 4 Your first histogram u rl als Now that we have an histogram We are not going to stop here Let s generate a scatter plot in three dimensions Just add two other metrics to the Used Metrics list You will notice that the text of the Compute Histogram button now becomes Compute Scatter Plot Just click it and you will have a scatter plot Here is the re
15. 000 Bu olmquist er Davic Nair Jesse Tversky Colin In the new subgraph we then select the Robertson node Again as above usetheAlgorithm gt Selection gt Reachable Sub Graph algorithm pick a depth of 2 to find all papers that cite a paper written by Robertson and save the resulting subgraph using the Edit gt Create Subgraph menu The final image shows the result of using the Algorithm gt Layout gt Hierarchical Graph layout U O _als You can now close this graph since we are going to use an other one for the following of this tutorial The next graph is similar to the this one but has coauthorship edges linking authors who write papers together You can download it and open it in tulip 4 3 2 What if any are the relationships between two or more or all researchers 4 3 2 1 Focusing on Two Authors Here we focus on the relationship between two authors in this case Robertson and Card To select them use the find tool with at the first time the regular expressions G Rob And at a second time the regular expression Card and the add option checked To move those selected nodes away from the main layout use the moving selection tool If you click on one of the node you will be able to move both nodes at the same time 7 http tulip labri fr samples GRSC tlp gz 65 U O ri als Select Card and Roberts at the same time Press Shift while clicking on a node Select all their neighbors by
16. 4 Eccentricity This plug in compute the eccentricity of each node eccentricity is the maximum distance to go from a node to all others In this version the value is normalized 1 means that a node is in the center of the network O means that a node is the more eccentric in the network The eccentricity will be saved in the viewMetric property of each node Algorithm documentation 3 2 3 1 5 Strahler The Strahler algorithm is very powerful It can for example point out important path in a graph by computing for each node the degree of ramification of its spanning sub tree Following is a graph with only one path You can see that each node have the same Strahler number 1 12 doxygen allPlugins html ClusterMetric 13 1 doxygen allPlugins html EccentricityMetric 25 Func tion al 17 ties But on this graph more the degree of ramification is important and more the number of strahler will be high Note that this graph could represent anything a program inclusion of sources files or a city road traffic 26 Func tion al 1 ties Parameters eAIl nodes If not checked the algorithm will choose a node a source node and will apply the algorithm to this node only If checked the algorithm will be applied to all nodes e Type This parameter can take 3 different values Register which will force the algorithm to give an indication on the degree of ramification for trees Stack that will force
17. 49 4 KS T wre see area lean ula Meh Gs Patel en ee PO ae ee ee os 52 MLET ESO eier ee ee eee eee eee 52 Al S C G Te TTT 52 AZ DAVE OPUONS reines ek Dee ee ee ls a as 53 ASAS ries 53 AD Improyins ALA NOU rta ii 53 4 2 1 Introduction 5 diia GS 53 As EEES SICA mPOA ON ini ds 53 42 3 USAS O Er ba QUES oia 54 AZ SNOWING abel uns ee AA Erde 58 AO SNOW IS IE C KIOL OLME regieren 60 AO COMCIUSION ud AAA Aptos orde 61 453 People IO WIS sd BR He A EA 62 43 12 Analyz ns ana thor essen ie ae aS 62 4 3 2 What if any are the relationships between two or more or all researchers 65 4 4 Statistics Panel not available in the downloadable binary versions requires configuration with enable stats gui when compiling Tulip from source code 0 c cece cence ence ene eee 75 14 1 Ina S Ee Te za ai A sde 75 4 4 2 Scatter plot and Histogram computation ccc ccc ence nen ene e ene nees 76 4 4 3 Statistics values and Augmented displays 2 0 cece cece ence rererere 80 444 Chisterine withthe statistics panel ers Es 83 111 Tulip User an _ual 4 4 5 Conclusion 1V List of Figures 21 2 OMA 100 Tab en ee ee Se I ee 10 22 DI Play Tab TTT 11 DEIS TEN eri oa iaa aaa 12 SL BMAP Ta e sea ea essen 49 IA D RECAMARAS Reber 50 3 3 TEXTO Renden dados ea bates ead ty deed paa 50 AL E E T Dase test sel SA AICO ae Boned E ap oa Eee doe heen od ea eee eka 76 A 2 The metrics availabl
18. 7 New 3D View A very useful tool in Tulip is the View gt New 3D View This tool will create a new window with the same name and the same graph as before But this window is not a copy of the original one It is just another view of the graph For example if you zoom in forward a node on the second window nothing will change on the other one But if you delete a node on the second window 1t will be deleted in the original window a a nodes d edges Chapter 3 Functionalities 3 1 Management of Graphs Tulip software offers a way to create and manage graphs The main window enables to have several 3D views to show differents graphs The menu bar enables the user to create a new view In there and with the mouse toolbar the users can create nodes and edges at the place where the pointer is When you have a graph and you want to keep traces of the graph you can save it in the t 1p format of Tulip Software An other option is to export it in the GML format for the graphlet system a toolkit for graph editors and graph algorithms Then you can save as an picture the result you had Tulip supports different formats BMP EPS JPEG PBM PGM PNG PPM SVG XBM XPM Tulip could generate a graph from data importation Examples of importation e Adjacency Matrix a form of representation of graphs Please visit Wikipedia Adjacency Matrix for more details e File System make a graph with your file sy
19. Color will be the color of the node that has the lowest value according to the Property field eColor2 Color2 will be the color of the node that has the highest value according to the Property field Let s take an example As you can see here 1s a graph where no metric values has been computed 1 E 2 Cu Ee N Ent e as OS E hh a ie E AEA k aP N REA DT R a A Ni 9 Jd doxygen allPlugins html SpanningTreeSelection 2 Func tion al 1 _ ties After applying the degree algorithm the graph gets colors If you do not have any colors on edges see if you have checked the Color interpolation in the rendering parameters window CTRL R After applying the Metric mapping algorithm type checked colormodel equaled to 1 Colorl a kind of red and Color2 a kind of green we will obtain the following graph 23 Func tion al ties 3 2 3 Measure Measure algorithms are used to compute different metrics on edges or nodes The computed values are assigned to the viewMetric property 3 2 3 1 Graph 3 2 3 1 1 Betweenness Centrality Betweenness is a centrality measure of a node within a graph Nodes that occur on many shortest paths between other nodes have higher betweenness metric than those that do not As this algorithm will compute a global measure it can take a long time to finish See Widipedia Betweenness for more details Algorithm docum
20. GML or TLP equivalentto Save as Select File gt Export and the format of your choice then choose the file name and location 4 1 3 Algorithms This part explains how to apply an algorithm to a graph Previously you have created or imported a graph Select Algorithm gt Layout for example and an algor thm Hierarchical gt Hierarchical Graph for example In this case we use an algor thm dealing with the layout of the nodes and the edges It is possible to apply all other kinds of algorithm Some layout algorithms may not apply to your graph if it does not belong to the right category of graphs With the Bubble Tree layout you can not display a grid If it is not valid a pop up message will displayed explaining the problem 4 2 Improving a layout 4 2 1 Introduction In this tutorial we will show you how to use layouts algorithms and graph properties to obtain a nice an clear graph To do so we will first import a file system structure and then use the graph properties to find specific files cpp or hpp 4 2 2 File system importation To import a file system we need to selectthe File System Directory importation tool which is in the menu File gt Import gt Misc A file browser dialog will pop up to select the root directory that you want On this dialog you just need to select a directory for instance your documents On Windows My Documents The importation plug in will work for some time and a tree g
21. Metric property e Layout this submenu is populated by layout algorithms which allow to display graphs using different types of drawings For example the Circular algorithm places all nodes of a graph along a circle Before After eSize this submenu is populated by size algorithms which allow to compute the size the viewSize property see Section 3 3 Properties of graph for more details of the graph elements e General this submenu is populated by more general algorithms for computing properties subgraphs quotient graphs groups For example the Equal Value algorithm create subgraphs for which the included elements have the same value for a choosed metric property For more information please visit Section 3 2 Algorithms e Graph This menu is composed of 2 sub menus e Tests This sub menu contains tools able to say if the graph obey some constraints e Simple Is the Graph Simple For more information please visit Wikipedia Simple graphs eDirected Tree A directed tree is a directed graph which would be a tree if the directions on the edges were ignored Some authors restrict the phrase to the case where the edges are all directed towards a particular vertex or all directed away from a particular vertex For more information please visit Wikipedia Directed Tree Free Tree A tree without any designated root is called a free tree For more information please visi
22. Tulip User Manual Tulip User Manual Table of Contents IS REST 6 PIO en oia ea nee ee 1 22 Grapliie Intertace mic sen Dee a eier 2 ZA ON window Menus adri ee ehe ee se 2 22 Mouse Interaction Toolbar y a LE I AAA 4 23 3DOVENIW AS AS O E ES 6 24 Rendering Parameter at o dicas 6 ZO MOE rd ari ba ado 8 ZN S 151 A AAA RI E AAA A AA pe as 8 Ds CMC meri o io ee N DELETE 9 Dee est R O O RAR 9 2 5 4 Statistics not available in standard version o 10 DB VIENSMARCOM he ed s a ES Rt ts Re 13 ZO Popup Mentor Crap VIEW oi AAA AAA 14 ZA ANETO dead 15 SS PUDCUOMANUIES adas da 16 3 1 Ma as ment OF Gran sisi A AER AAA 16 Sl Ihe Pin Role AS A ITA A An 17 3 2 AOS ie reos AM ES ea ese ee ee ee Ss ee 17 527i Selecon Alsonthiis rasen AAA een 17 5 222 Color AlSOMMMS EAS aed ias 22 FI L L TTT 24 OLAV OULU ET 34 VIII sad tov nh hud an waive Goce Ou aos tocas Nene 42 O52 A ee ake EEE s aus E EE EEE 43 3 3 POP CI ICG OR CRAP Ms os ee en een cae Gs 44 S ne ee ee ee es Res 44 33 2 2 sins Properties Bears Bee ea ye 45 3 4 HETAC DY este era pre oe Be Ra Re a Pe Gees 46 A ehe ee ee 46 3 42 Creatine SuboTapns OF Groups senken sa reed 47 3 4 3 Deleting Ungrouping a subgraph or a Group 2 nenn 48 JAA sine Sub etaplis Or e sense 49 K Alsorithms that crealessubstaphs zus ER He a aeeeotes 49 3 5 Statistics Panel not available in standard version 0 0 ccc cee eee e nen ens 49 For Test AT near ei a er nee ee
23. a clustering algorithm Dendrograms are often used in computational biology to illustrate the clustering of genes The algorithm takes 4 parameters e node size size of the node will depend of the metric that you choose The Algorithm will consider that parameter so that no nodes overlap themselves This can be useful if you want a node to be far from the others just take a new size Metric and give a higher value to that specific node e orientation up to down left to right right to left or down to up e layer spacing space between the levels of the Tree e node spacing space between sibling nodes 30 Anxvoen allPlno doxy gen allPlugins html ConeTreeExtended JT Func tion al 15 _ties Algorithm documentation 3 2 4 2 4 Hierarchical Tree R T Extended The hierarchical tree layout looks the same that the dendrogram layout or the improved walker layout but takes an other parameter edge length e node size size of the node will depend of the metric that you choose The Algorithm will consider this parameter so that no nodes overlap themselves This can be useful 1f you want a node to be far from the others just take a new size Metric and give a higher value to that specific node e edge length this parameter can take a property of type int and will be used to place a node on a specific layer If its value is 1 no thing will happen but if its value is 2 the node will be placed on the next layer
24. algorithm will count for all nodes its number of edges without ramification Following are two graphs On the left one you can see that the root has 3 edges without ramification But on the right graph all nodes without considering leaves have only 1 edge without ramification Func tion al 17 ties JEF This algorithm can be useful to see how the graph is formed Indeed if the root has a small value t w ll mean that the graph has a good ramification But if the root has a high value it will mean that the graph a lot of segments 3 2 3 3 7 Tree Arity Max Compute the maximum outdegree of the nodes in the subtree induced by each node To access to the degree of a node it is recommended to use directly the degree function available in each Graph Algorithm documentation 3 2 3 4 Misc 3 2 3 4 1 Id The id algorithm will for each node and edge save their id number in their viewMetric Property For example if we have a node called Node 9 its id number will be 9 Algorithm documentation 3 2 3 4 2 Random Random will just save a random number from 0 to 1 in the viewMetric property of each node and edges Algorithm documentation 3 2 4 Layout Warning Some of the following algorithm have no effect if the option Force Ratio is checked 3 2 4 1 Planar 3 2 4 1 1 3 Connected Tutte This algorithm can only be applied to 3 connected graphs A graph G is said to be 3 connected if there does not
25. algorithms can made subgraphs A subgraph share its elements with the graph it is just a part of the graph It is possible to add properties for the subgraph only or to use the inherited properties For more information please visit Wikipedia Subgraphs 3 4 1 2 Groups Some graph can be a subgraph of an other graph This kind of hierarchy enables to assign a graph to a node 3 4 1 3 Meta graph A meta graph is a graph that contains meta nodes 3 4 1 4 Meta node A meta node is a node that contain a group A meta node can contain refer to the root graph Fractal effect 3 4 1 5 Screen shots Following is an over view of a graph hierarchy The graph 41 http en wikipedia org wiki Glossary_of_graph_theory Subgraphs 46 Func tion al 1 ties Property Element Bi eres hey Subgraph Hig Mb nodes Mb iger Graph id Er EHET CM 0000017 groups Oe 0000006 GOZ qp 006007 MEH O Oo The subgraph and the meta node into Echter Property Element Hierarchy bpp Ha He ride Abe Sap Metanode The group rel Jiti ge ERA LEER HARD 3 4 2 Creating subgraphs or Groups 3 4 2 1 Creating a subgraph To create a subgraph follow these steps Func tion al 1 _ties e1 Select a few Nodes with the selection tool Shift click will add a node to the selection To select the edges that are between the selected nodes use the Induced Sub graph algorit
26. bGraphSelection 18 Func tion al 17 ties By creating a sub graph we get a simple graph which is much more easy to read Please visit Wikipedia Kruskal s algorithm 7 for more details Algorithm documentation 3 2 1 3 Loop Selection This selection algorithm is able to select the loops of a graph A loop is an edge that has the same source and target http en wikipedia org wiki Kruskal 27s_algorithm 4 led doxygen allPlugins html Kruskal 19 Func tion al 1 ties Algorithm documentation 3 2 1 4 Multiple Edge This selection algorithm highlights the multiple edges also named parallel edges in a graph Two edges are parallel only if they both have the same target and same source Algorithm documentation 3 2 1 5 Reachable Sub Graph This selection algorithm enables to find all nodes and edges at a fixed distance of a set of nodes It takes three parameters Distance number of edges to follow eDirection 0 means directed 1 reverse directed 2 undirected eStarting nodes the selected nodes of this selection property boolean will be used as starting nodes In the following example distance equals to 1 direction equals 0 and the starting node is the one in the center Before ll doxygen allPlugins html LoopSelection ce doxygen allPlugins html MultipleEdgeSelection 20 Func tion al _ties After Algorithm documentation 3 2 1 6 Spanning Dag
27. chy in the info editor window and select the subgraph GRCite You need to delete the other sub graphs by doing a right click on there name and then remove This graph represent the relations between authors conferences and papers To distinguish paper conferences and authors we will re color them e Select all papers Press on Ctrl F to display the find tool In the Input Property field select the property type And on the line below set the filter function to and the filter value to 0 before clicking on the Find button e Re color the nodes in red Select the tab Property in the info editor Check the selected only option Select the property viewColor and by clicking on the button Set all choose the red color Repeat the actions above for authors type 2 and conferences type 1 with other color blue yellow You should obtain something like this froot Documents toto tip Select an author Let s pick a single author to investigate in this case George Robertson First we interactively select that node by hitting Ctrl F for the find tool choosing the titleshort property the as filter fuction and the regular expression G Rob as filter value We then quickly check to see how he is connected to the entire graph by temporarily moving that node away from the others to see roughly how many edges are attached to it Following is what you should get 4 http tulip labri fr samples GRCi
28. des or the edges that are not related to the structure For example if we build the map of a region and the nodes represent the towns the label property can be used for the name of town But it is not possible to determine the name with the structure of the graph this kind of property is extrinsic For each graph Tulip provides a set of properties used by the renderer engine all begin with the view prefix by convention viewColor viewLabel viewLayout They are updated during the computation phase of the plugins In the other hand it is possible to define properties to store informations relative to the graph The number of this created properties are not limited Following is the list of rendering properties eviewBorderColor Color of the border of an edge or a node eviewBorderWidth Width of the border of an edge or a node eviewColor Color of an edge or a node eviewLabel Label of an edge or a node eviewLabelColor Color label of an edge or a node eviewLabelPosition Label position x y z of an edge or a node eviewLayout Position x y z of a node or vector of the bends positions of the edges eviewMetric Result value of the last measure Section 3 2 3 Measure algorithm applied eviewRotation Rotation 0 to 360 of a node or an edge eviewSelection Selection equals true if the node or edge is selected False if it is not eviewShape Shape of anode or a graph eviewSize Size height wid
29. e in thestatistics panel rss ee Chee eae 76 AS A single meric toran histogram re ea ee 71 e R ETH Mist MISCO RANE zus near een ie eg ers 78 4 5 Scatter plot generated from the three metrics a ed di a E 79 4 6 Click on the button Compute Result to enable the tab ec ceee ees 80 4 1 Checking Averase on the display taD san es EE E hues ehaeees 81 4 83 Iheaverase Ol the Scatter DIOL zer re ie 82 4 9 Selection OF LHe Clusters valle seat een 83 ALO The clusters Plane dis RA ba 84 4 11 The new clusters alter Statistic dl ustenng eu a aa aes 85 Chapter 1 Introduction The research by the information visualization community show clearly that using a visual representation of data sets enables faster analysis by the end users Tulip created by David AUBER is a contribution of the area of information visualization InfoViz Even if the Tulip framework enables the visualization the drawing and the edition of small graphs all the parts of the framework have been built in order to be able to visualize graphs having to 1 000 000 elements A visualization system must draw and display huge graphs enables to navigate through geometric operations as well as extracts subgraphs of the data and allows to change the representation of the results obtained by filtering gy Edt Swain Graph View Dinge Opims Windows Help us Aves exe Chapter 2 Graphic Interface 2 1 Main window Menus File Edit Algonthm Graph View Dialogs Opt
30. e two metrics in the Used Metrics list and Eigenvectors is enabled only if you have three metrics in the Used Metrics list The checkboxes next to each groupboxes except the Variance one are used to display on the Histogram Scatter plot the result of the group For example checking the checkbox next to Average will display the average point on the graph an Axis Point in red c f GlAugmentedDisplay in the developer handbook Figure 4 7 Checking Average on the display tab u o _als Sigma 1 42 24 41 19 33 Min 1 0 0 Max 9 109 109 inear Regression Function 2 metrics Ordinate in the beginning 0 Slope 0 Eigen Vectors 3 metrics vl 1 0 66 6 1 177 we 1 0 6138 1 198 1 v3 1 1 558 0 03662 Figure 4 8 The average of the scatter plot qu _als Every augmented display works the same way You will just have to click on the checkbox next to the group to enable the display of the result Note that you can t display the Variance since this result can t be represented in an interesting way on the graph use instead the standard deviation Now that you know how to display the statistics results you will see how to clusterize the scatter plot histogram from these values 4 4 4 Clustering with the statistics panel The last part of this tutorial will teach you how to clusterize from the statistics results previously computed Firstly switch to the Clustering tab The C
31. entation 3 2 3 1 2 Cluster This algorithm can only be used on simple graphs graphs with no loops The cluster algorithm is a measure algorithm that can determine whether or not a graph is a small world network The clustering measure is a local measure that gives the connections rate of a node and its neighbors Let s take an example 10 http en wikipedia org wiki Betweenness Woy doxygen allPlugins html BetweennessCentrality 24 Func tion al 17 ties On this graph and by looking at the clustering measure you can see 2 communities nodes in blue and a hub node in yellow the hub is the only way to connect the two communities For more details please visit http en wikipedia org wiki Clustering_coefficient Algorithm documentation 3 2 3 1 3 Degree This algorithm will save the degree of each node in its viewMetric property It takes two parameters e Type Is the type of degree you want to compute In Edges that comes onto the node Out Edges that are going away from the node InOut Using both in and out e Metric This parameter can take all double properties but by default it will take None viewBorderWidth viewMetric and viewRotation If you choose none the degree of the node will be the sum of the edges If you choose the viewMetric value degree of the node will be the sum of edges wiewMetric property As of viewBorderWidth and viewRotation 3 2 3 1
32. essing on the mouse right button press Ctrl key when mouse pressing on Mac e Select the property you want to modify viewLabel e Click on the checkbox named Filter The selected element just appears in the table above e Click on Set all and write the text you want to display Hey If you uncheck selected only all nodes are in the table It is possible to do the same thing with the values of edges You just have to click on the tab named Edges There is an other solution to modify the value of one node or edge e First select the mouse toolbar operation then click on the node or edge you want to update e The Element tab of the Info Editor subwindow is then selected It displays the informations of the element you clicked on 3 3 2 2 Management of properties The bottom of the Property subwindow enables to manage the properties For each graph as explain before a set of display properties already exists If you want to create a new property e Click on the New button e Select the type of property String other possibilities are Color Integer Layout Metric Size Selection e Type the name of the new Property e g mylabel 45 Func tion al ties For removing a property you just have to select the property and click on the button named Remove When deleting properties used by the render engine those properties will be temporary removed from the list but still continue to exist Note that it is not pos
33. et Small world navigation 1s useful when exploring an unfamiliar graph to quickly find the structure of complex components The eccentricity metric Al gorithm gt Measure gt Graph gt Eccentricity which measures whether nodes are peripheral here in yellow or central here in blue guides us to complexity immediately This metric 1s O n 3 but the small world decomposition simplifies the graph making the computation tractable The picture shows zooming in towards the node that has many blue lines leading to it 1 http tulip labri fr samples ConfAuthRecSmallWorld tlp gz 73 u O _als Harian Foote Henry Lapse Helwig tisser We then jump inside that cluster Select the metanode Right Click Go inside which is itself a small world graph We once again zoom towards the most central node with many blue edges where we see a cluster that has the Info Vis 96 conference and all the authors who only published the infovis community in that year 74 Tutorials We see this star shape small world decomposition only for the InfoVis symposia because of the nature of this dataset it is only the InfoVis symposia that have a complete set of authors and papers available 4 4 Statistics Panel not available in the downloadable binary versions requires configuration with enable stats gui when compiling Tulip from source code 4 4 1 Introduction This section will explain how to use the statistics panel i
34. exist a set of 2 nodes whose removal disconnects the graph Triangle Layout Algorithm documentation 3 2 4 1 2 Mixed Model Create a planar sub graph with polylines with a good angular resolution which will make the graph clear and easy to read Algorithm documentation 8 3 2 4 2 Tree doxygen allPlugins html TreeArityMax 25 _ doxygen allPlugins html IdMetric 26 J doxygen allPlugins html RandomMetric 27 J doxygen allPlugins html Tutte 28 d doxygen allPlugins html MixedModel 34 Func tion al ties To represent a tree a hierarchical layout is the easiest way to understand the tree structure But this layout has a big weakness when the tree has a lot of nodes it does not effectively use the space where the tree is displayed That is why we need different layouts 3 2 4 2 1 Bubble Tree The Bubble Tree algorithm can be use to change the layout of a tree On the new layout a node will be on the center of a circle and its children will be on the circle This new layout has the following properties e The edges should not cross each other e The polyline used to draw an edge should have the least possible bends e The minimal angle between two adjacent edges of a node n should be nearest to 2pi deg n This property will improve the angular resolution e The order of children of a node should be respected in the final drawing Here is an example The following graph has the default layout hierarchical
35. f 26 authors that have had 12 U O Tl als a relatively strong impact The third cluster contains a group of 7 influential authors Chi Bederson Eick Rao Pirolli Ward and Brown and the fourth cluster Roth Robertson Keim and Stasko is yet more central The fifth cluster is the single node of Mackinlay and the last one is Card and Shneiderman Our automatic clustering method clearly yields very believeable results in this case In the last section we will use an other graph Please download it and open it in tulip 4 3 2 5 Hierarchical Structure of Interauthor Connections To be able to see the labels within metanode check the metanode option in the Rendering Parameters dialog Ctrl R The clusters have been computed using the Algorithm gt General gt Strength clustering algorithm The overview image from the previous section showing the graph of all authors and papers is extremely cluttered In the previous task we show one way to extricate more information by finding the most important items via convolution clustering Another clustering approach small worlds clustering allows us to instead navigate through a hierarchical subdivision of the entire dataset The simplified overview allows us to understand the graph s high level structure The strength metric computes the number of cycles of length 3 and 4 passing through each edge normalized by the maximum possible value The first image shows the clustered datas
36. graph The subgraphs created with the group wont be deleted 3 4 3 2 Subgraphs To delete a subgraph left click on 1ts name in the Info editor gt delete Func tion al lies Note Deleting a subgraph has no effects on the root graph 3 4 4 Using subgraphs or groups 3 4 4 1 Subgraphs 3 4 4 1 1 Moving a node in a subgraph If you move a node in a subgraph the same node will be moved in the root graph 3 4 4 1 2 Using an algorithm on a subgraph If you use a layout algorithm on a subgraph all changed layout properties will be applied to the root graph If you use a Measure algorithm on a subgraph New local properties w ll be created Those properties wont be applied to the root graphs 3 4 4 2 Groups Changes on groups wont be applied to the root graph unless you ungroup the group 3 4 5 Algorithms that creates subgraphs You can find those algorithms in the menu Algorithm gt General e Equal Value Section 3 2 6 2 Equal Value e Hierarchical Section 3 2 6 3 Hierarchical e Quotient Clustering Section 3 2 6 4 Quotient Clustering e Strenght Section 3 2 6 5 Strength 3 5 Statistics Panel not available in standard version Tulip also provides a simple statistics interface which allows the user to compute Histograms Scatter Plots Augmented Displays and Clustering The computation of Histogram and Scatter Plot depends on a number for metrics chosen by the user fr
37. hm e2 Create a subgraph from the menu Edit gt Create Subgraph or from the keyboard Ctrl Shift G Give it a name You will be able to find your new subgraph in the hierarchy onglet of the info editor window 3 4 2 2 Creating a group To create a group follow these steps e1 Select a few Nodes with the selection tool Shift click will add a node to the selection To select the edges that are between the selected nodes use the Induced Sub graph algorithm e2 Create a group From the menu Edit gt Create group or from the keyboard Control G A warning saying Grouping can not be done on the root graph a subgraph will be created may pop up if it does just click OK You will be able to find your new group in the hierarchy onglet of the info editor window Severals subgraphs will be created e A copy of the root graph called groups containing a meta graph with a new meta node pointing to our group e A subgraph which is our new group 3 4 3 Deleting Ungrouping a subgraph or a Group 3 4 3 1 Groups 3 4 3 1 1 Delete To delete a group left click on 1ts name in the Info editor gt delete Note By deleting a group all nodes in this group will be deleted as well whereas the meta node will still exist 3 4 3 1 2 Ungroup To ungroup a group select 1t Left click gt Ungroup Note By ungrouping a group all the layouts properties of the group s nodes will be applied to the root
38. ies The strongly connected components of a directed graph are 1ts maximal strongly connected subgraphs These form a partition of the graph Here 1s an example Before After 3 2 3 3 Tree To use the following algorithms the graph has to be acyclic A graph is acyclic if it contains no cycle 3 2 3 3 1 Dag Level The dag level algorithm will compute the depth of each node as on the following example Func tion al ties Algorithm documentation 3 2 3 3 2 Depth The depth algorithm will compute for each node the maximum number of edges to follow to find a leaf Algorithm documentation 3 2 3 3 3 Leaf The leaf algorithm will compute for each node its number of leaves Here is an example 20 11 doxygen allPlugins html DagLevelMetric 2 doxygen allPlugins html DagLevelMetric Sl Func tion al 17 ties Algorithm documentation 3 2 3 3 4 Node The Node algorithm will sum for each node the number of its children nodes plus him self Algorithm documentation 3 2 3 3 5 Path Length This algorithm will count for each node the number of paths that goes through it Here is an example 22 J doxygen allPlugins html LeafMetric 23 d doxygen allPlugins html NodeMetric 32 Func tion al 17 ties 3 2 3 3 6 Segment A segment is a set of nodes that are all on one and only path The graph showed on the left side of the example is a segment The segment
39. ions Windows Help The main window of Tulip software is composed of several subwindows and a menu bar eFile this menu is used for usual file operations New Ctrl N Open Ctrl O Save Ctrl S Save As Ctrl Shift S Print Ctrl P and Exit Ctrl Q Others are added e Import this submenu is populated by import plugins eFile Plugins allowing importation of graph files in different format such as Adjacent Matrix gml dot graphviz or tlp tulip default file format e Graph Plugins allowing the creation of randomly generated graphs of different types e Misc Plugins to capture the tree structure of a file system directory or the graph structure of a web site eExport this submenu is populated by export plugins allowing to save a tulip graph accordingly to a specified format By default Tulip is able to export in GML and TLP formats e Save as picture this last menu gives the choice between different picture formats BMP EPS JPEG PBM PGM PNG PPM SVG XBM XPM in wich graphs can be exported to eEdit this is composed of tools Cut Ctrl X Copy Ctrl C Paste Ctrl V and Find Ctrl F which affect the selected elements This menu contains also Select All Ctrl A Delete selection Del Deselect all Ctrl Shift A Invert Selection Ctrl D Create group Ctrl G Create subgraph Ctrl Shift G More details on the Find tool The find tool has 4 options e Replace Replace the current selection nodes or edges already selected
40. l create a metagraph The metanodes will be the subgraphs that already exist and an edge will be created between two metanodes f and only if it exist an edge whose source is a node of a subgraph and the target a node of an other subgraph Parameters eoriented This parameter indicates whether the graph has to be considered as oriented or not enode function This parameter enables to choose the function used to compute a measure value for a meta node using the values of its underlying nodes eedge function This parameter enables to choose the function used to compute a measure value for a meta edge using the values of its underlying edges e edge cardinality This parameter indicates whether the cardinality of the underlying edges of the meta edges has to be computed or not If yes the property edgeCardinality will be created for the quotient graph doxy gen allPlugins html HierarchicalClustering 43 Func tion al 1 _ties Algorithm documentation 3 2 6 5 Strength The strength algorithm will recursively create subgraphs that are nested small worlds Wikipedia small worlds gt Algorithm documentation 3 3 Properties of graph In Tulip there is a way to assign properties to each node or edge of the graph Tulip defines two kinds of property intrinsic and extrinsic The first represents the properties computed relatively to the structure of graphs But it is possible to assign values to the no
41. l projection enables disables the orthogonal projection If not checked the perpsective projection is used eBackground color enables to choose a color for the background of a graph view Graphic er _face 2 5 Info Editor This subwindow is divided in four tabs Property Element Hierarchy Statistics not displayed in the standard version 2 5 1 Property This tab enables to display the properties of nodes and edges as a table It is composed of two parts The one of the top of the tab displays all the values of nodes or edges for the selected property choosen in the lists at the bottom of the tab It is possible to display only the values of the selected elements by using the selected only box The user can modify directly a value by clicking on the value in the table It is possible to set all the nodes or edges value with the Set all button ifthe selected only box is checked this will only affect the selected elements An other possibility is to set as labels the values of the selected property by clicking on the To labels button The bottom part of the tab displays the lists of all the local and inherited properties of a graph An inherited property is a property which is defined for an upper graph in the hierarchy of graphs see Section 2 5 3 Hierarchy Info Editor x Property Name Nodes Edges Inherited By a right mouse button press press Ctrl key when mouse pressing on Mac on a row of the tab
42. le values you can display a pop up menu allowing some actions on the graph element corresponding to the table row edge 11003 Add to Remove from selection Select Delete Properties Graphic n er _face e Add to Remove from selection this allows to change the selection state of the element e Select the current element replaces the whole selection e Delete this permanently removes the element from the current graph Properties this shows the element properties in the Element tab see after For more details please visit Section 3 3 Properties of graph 2 5 2 Element This tab shows informations about an element of the graph node or edge previously pointed using the mouse toolbar operation At the top you can find the type of the element and its id To follow here is the table displaying the elements properties and associated values As within the tables of the Property tab 1t 1s possible to update the values within this table Info Editor Node 0 Property Value viewBorderColor viewColor viewLabel viewLabelColor A viewLayout 7 2 7 28 0 viewMetaGraph viewRotation viewSelection false viewShape 3D CubeQutLined viewSize 1 1 1 viewTexture 2 5 3 Hierarchy This tab shows the inclusion relationships betweeen the different existing subgraphs and groups of a graph All of them could be created with the Tulip tools A hierarchy of graph is often the
43. les Which is the biggest or which is the smallest But we can also see the structure of directories since files and directories are nested nodes See Wikipedia Tree Maps for more information An other layout can be useful the Improved Walker 4 2 3 3 Improved Walker layout This layout can be find in the Algorithm gt Layout gt Tree gt Improve Walker Use the following parameters e Node Size viewSize e Orientation Left to right e Orthogonal Checked e Layer Spacing Default value e Node Spacing Default Value You should see a tree looking like this 2 http en wikipedia org wiki Tree_map 57 As you can see the improve walker layout is just a hierarchical layout It is very useful to understand the tree structure of a file system 4 2 4 Showing Labels First in the Rendering Parameters dialog Ctrl R check the nodes box for the Visibility option We will now try to add labels to the nodes To do so select the node property called name in the info editor window click on the button To Labels You should now see a graph looking like that ee FI HG 2 eee P HE As you can see the labels don t fit in nodes and it is very hard to read the graph To fix this problem press Ctrl R in the Labels box the field Type must be equal to 3D Then apply the Algorithm gt Size gt Fit To Label algorithm You should obtain something like this qu rl als By zooming in
44. llPlugins html HierarchicalGraph 42 Ja doxygen allPlugins html GeneralGraph3 D 42 Func tion al 1 ties 3 2 5 SIZe 3 2 5 1 Auto Sizing The auto sizing algorithm will resize nodes and edges of a graph so that the graph gets easy to read The size of a node will depend on the number of its sons 3 2 5 2 Fit to label Fit to label will resize nodes and edges so that labels fit in nodes 3 2 5 3 Metric Mapping The size of the nodes will change according to a metric 3 2 6 General 3 2 6 1 Convolution Convolution clustering is an approach to partitioning a graph that gives the user interactive control over how many clusters to create Tulip calculates a density function based on the chosen metric displays a convolution of its histogram and partitions the graph according to the humps in the histogram 3 2 6 2 Equal Value This algorithm will create sub graphs in which all nodes or all edges not both a the same time have the same value 3 2 6 3 Hierarchical This algorithm will divide the graph in 2 different subgraphs the first one will contain nodes that have the viewMetric value under than a certain limit and the other one in which nodes will have a the viewMetric value higher than the limit Then the algorithm will be re applied to the subgraph the one with higher viewMetrics until the subgraph contains less than 10 nodes Algorithm documentation 3 2 6 4 Quotient Clustering This algorithm wil
45. n Tulip The tutorial is composed of 3 main parts Firstly you will see how to generate a scatter plot or an histogram from a graph In a second part you will see how to enable augmented displays on the graph And finally you will see how to clusterize the graph from the statistics values previously computed 75 Every screenshots that will be shown in this tutorial are based on this tree Figure 4 1 Statistics base test set a tree 4 4 2 Scatter plot and Histogram computation The first thing to understand about the statistics panel is how to generate an histogram or a scatter plot from the graph The computation of histogram scatter plot is based on metrics So in a first time you will have to compute metrics In the example we have computed three metrics Arity DAGLevel and Depth The new metrics are automatically updated on the Available Metrics list on the Stats panel Figure 4 2 The metrics available in the statistics panel U O Tl als Auto Shape Conversion Cube rMeincs Available Merrics Anity DAGLevel Depth yakleinic vidna Hc anp Add Remove Used Metrics Discretization Step x Discretization Step y Discretization Step z Change to Histogram Compute Results Now that you have some metrics available You can add them to the Used Metrics list simply using the Add and Remove buttons The number of dimensions of the result
46. ng algorithm whenever a measure algorithm has been run e Morphing Enables the Morphing from a layout to an other e Tooltips Enables the display of tooltips on nodes or edges e Grid Shows the grid configuration dialog e Help in this menu you can find informations about the software and the way to make your first steps 2 2 Mouse Interaction Toolbar This toolbar allows to select the mouse operation you want to perform Operations are listed and explained from left to right of the toolbar 8 http en wikipedia org wiki Planar_graph 7 http en wikipedia org wiki Simple_graph Simple_graph 10 nttp en wikipedia org wiki Acyclic_Graph 11 http en wikipedia org wiki Connected_graph 12 http en wikipedia org wiki Biconnected_graph 13 http en wikipedia org wiki Directed_tree 4 Y 3D Navigation This tool enables the 3D navigation on a graph using the mouse movements left button pressed the available operations are translate rotate zoom zoom and pan Translation 1s the default operation and can also be activated using the Arrow keys rotation 1s activated using Shift key zoom is activated using Ctrl key Alt key on Mac zoom and pan is activated using the wheel of the mouse APPLE key on Mac Warning the last operation is mouse position centered i e it attempts to translate the last 2D or 3D position of the mouse to the center of the view Get Information when this operation is selected if you click
47. om 1 to 3 and a discretization step one given per metric Finally the clustering is performed from a clustering plane specified by the user with a plane equation 3 6 Text Rendering It is possible to assign a label to each element of the graph Tulip can display them with three methods 3D and texture for node labels bitmap for node and edge labels Figure 3 1 Bitmap Rendering 49 Func tion a ties WwWww tu ll D sofitw are orgy 2 a al E Sh Figure 3 2 3D Rendering Figure 3 3 Texture Rendering Func tion a ties In a future version of Tulip It will be possible to create labels with XML tags like the HTML rendering Some tags will be available in order to allow the user to organize the content of the labels Chapter 4 Tutorials 4 1 First Step In this part the goal is to help you to simply make a graph and to save your work 4 1 1 First graph display 4 1 1 1 Importation of a graph e Select the File gt Import item e Select a method of importation Grid approximation for example Do not modify the default parameters Here is displayed the graph with nodes red and edges black With the wheel of the mouse you can zoom on the graph to see a specific node In moving the mouse with its left button pressed you can translate the graph in the plane of the view pressing the key SHIFT for rotation and the key Ctrl Alt key on Mac to rotate around the z axis and zoom In order to
48. ombobox Clustering Value lists the available start for a clustering plane depending on what has been computed before Select Average Z you must have selected 3 metrics the plane coordinates will be modified according to the values of the average s Z coordinate Check the Display Clustering Plane checkbox The plane appears in transparent red showing you the future two clusters Figure 4 9 Selection of the clustering value qu _als Figure 4 10 The clustering plane U O Tl _als In order to have the good clustering you can modify the plane equation not really smooth will be enhanced in the next versions of Tulip to move the plane Finally to clusterize just click on the Clusterize button That s it The graph 1s now clusterized In order to ensure just check the Cluster Tree Figure 4 11 The new clusters after statistic clustering u Tl _als Info Editor neas groups tip u en 0001 subgraph_0002 4 4 5 Conclusion As a conclusion you have learnt how to use the statistics panel of Tulip As you can see obtain ing results is easy and fast If you have any question about that panel you can contact it s creator at lt maxime delorme gmail com gt
49. r Plot This layout can be used to see a correlation between 3 metrics parameters For example 1f we have a node with usedMetric1 0 usedMetric2 1 and usedMetric3 2 the node will be place in the space with the coordinates 0 1 2 Following is an example in which are 3 nodes Those 3 nodes have 3 Metrics called x y z Node 1 equals to 0 0 0 Node 2 equals to 1 1 1 and Node 3 equals to 2 2 2 We can see from the layout that our correlation follow a linear function Func tion al 17 ties 3 2 4 5 Force Directed Force Directed layouts will try to place nodes so that the distance in the graph metric of the edges should be the closest to the distance on the drawing Warning The previous property is not true at 100 3 2 4 5 1 Embedder HDE The HDE layout will only work on a 2D Mesh like graph Algorithm documentation 3 2 4 5 2 GEM Frick The GEM layout unlike the HDE layout works on all graphs But it can take a very long computing time if the graph has more than 2000 nodes Algorithm documentation 3 2 4 6 Hierarchical 3 2 4 6 1 Hierarchical Graph This layout will place the nodes of a graph as if the graph was a tree Algorithm documentation 3 2 4 6 2 Hierarchical Graph 3D This layout is the same that the Hierarchical Graph but in 3D Algorithm documentation 39 doxy gen allPlugins html Embedder 40 J doxygen allPlugins html GEMLayout AL doxygen a
50. raph will appear representing the file system chosen To follow the rest of this tutorial you need to download this tulip graph file Graph Load this compressed tulip file into the software File gt Open 4 2 3 Using other Layouts 4 2 3 1 Bubble Tree Layout This layout algorithm can be found in the menu Algorithm gt Layout gt Tree The bubble tree layout is very useful to notice directories that have the same structure In this section we will try to locate those directories To have a better view on the tree we will create a new 3D view Menu View gt New 3D view or press Ctrl Shift N When the new view is created we need to re organize the windows Menu Windows gt Tile Now that we can see the both views at the same time we will zoom in right window Select the magnifying glass tool and draw a bounding box on the left side of the graph Just like this l http www labri fr perso auber projects tulip samples filesystem tlp gz 54 TB R T zur mr N drre as EE E 15 9 Ir bN hampe B m we Laa ip haa Aleck He p NAA Hates Pe ot Y ON ei el U lip res ero La N As you can see two nodes looks very alike By using the Get Information tool we can get there ids Node 1965 and node 2009 Indeed those to directories have the same structure since they both contains plug ins source files We will now re center the view View gt Center View or Ctrl Shift C Let s say that we now want to study o
51. rarchical tree in which nodes does not overlap Algorithm documentation 3 2 4 2 8 Tree Map Shneiderman This layout is the same as the squarified tree map layout but the squarified tree map uses shadows to draw the tree Algorithm documentation 3 2 4 2 9 Tree Radial On this layout nodes of the same layer are placed on a circle whose center is the root Algorithm documentation 3 2 4 3 Basic 3 2 4 3 1 Circular On this layout every nodes are placed on a circle Algorithm documentation 3 2 4 3 2 Random Nodes are placed randomly in space 3 2 4 4 Misc 3 2 4 4 1 Connected Component Packing This layout groups connected components of the graph so that they do not overlap them selves and that lost space is minimized packing It takes 4 parameters er ral l doxygen allPlugins html SquarifiedTreeMap 35 JJ doxygen allPlugins html TreeLeaf 30 JJ doxygen allPlugins html TreeMap 37 td doxygen allPlugins html TreeRadial 38 doxygen allPlugins html Circular 40 Func tion al 1 ties e node size size of the node will depend of the metric that you choose The Algorithm will consider that parameter so that no nodes overlap themselves This can be useful 1f you want a node to be far from the others just take a new size Metric and give a higher value to that specific node e Rotation e Coordinates e Complexity Here 1s an example left before right after 3 2 4 4 2 Scatte
52. result of the computation of clustering algorithms Info Editor Subgraph Hierachy groups grp_00002 amp subgraph_0001 subgraph_0002 grp_00003 grp_00004 grp_00005 grp_00006 grp_00007 By a right mouse button press press Ctrl key when mouse pressing on Mac in the hierarchy display you can display a pop up menu allowing to remove clone rename a graph subgraph or group 2 5 4 Statistics not available in standard version The statistics panel is composed of three main parts Computation Display and Clustering It allows the user to compute a histogram or a scatter plot from a graph and one up to three metrics The display part of the panel is used to display on screen the statistics main values as Average point Standard deviation Bounding box Linear Regression and Eigenvectors The clustering part is used to display a clustering plane from a statistical value previously computed and to separate the graph into two new clusters what is above the clustering plane sup and what is under the clustering plane inf Figure 2 1 Computation Tab Graphic n Discretization Step w 1 Discretization Step y 1 Discretization Step z Figure 2 2 Display Tab Graphic n er ace Sigma 2 88 0 Min 1 0 Max 16 0 near Regression Function 2 metrics Ordinate in the beginning 0 Slope 0 Eigen Vectors 3 metncs vl 0 0 0 v 0 0 0
53. rithm gt Color gt Metric Mapping algorithm Finally we color papers in white This layout shows the branching structure of the dataset 68 U O ri _als To distinguish authors and conferences Select all authors nodes of type 2 and set their viewLabelColor property to red 69 U O _als 4 3 2 3 Central Authors and Conferences Top Conferences It is very simple to see top conferences since they are the ones where the number of authors is high The Metric Degree will help us to highlight them A1gorithm gt Measure gt Graph gt Degree 70 U O ri _als 4 3 2 4 Central Authors and Conferences Top Autors Run the Algorithm gt Measure gt Graph gt Strahler algorithm to see strong ties between conferences and authors Then run the Algorithm gt General gt Convolution the value of the discretization parameter should be near 30 to obtain 5 clusters Picture 1 to obtain the following clusters Picture 2 71 U O Tl _als 4 Convolution Clustering Parameters Width Discretization Cancel froot Documents Co root Documents Co froot Documents Co Fim froat Documents co i ock Mackinlay The Strahler Convolution clustering yields five clusters according to increasing centrality The first cluster is mostly yellow and contains most of the data The second cluster contains a next tier o
54. s defined when pressing the mouse left button the opposite corner is defined when moving the mouse and the zoom operation is performed on the desired rectangle when the button is released OK Delete element allows to delete a node or edge by a simple click The deleted node or edge is the one under the mouse when you clicked Add node when it is selected you can add a node in the graph by a simple mouse click on the current graph view The node is placed at the coordinates corresponding to the mouse position when you clicked Add edge when it is selected you can add an edge in the graph by mouse clicking first on the source node then on the target node 2 3 3D Overview This subwindow always shows an overview of the current graph view 3D Overview a A aenn BERRE o wee The part of the graph which is visible in the current view is inside a black bordered frame In order to see a different part of the graph in the current view you can move the frame over the desired part To achieve this when the mouse is inside the frame just move it with the left button pressed A mouse left click with the Ctrl key pressed Alt key on Mac displays the Rendering Parameters dialog see Section 2 4 Rendering Parameters 2 4 Rendering Parameters All actions in this dialog are just performed for the current view window Labels Visibility nodes edges metanodes Type metric ordering Density of lt lt
55. sible to remove inherited properties The last feature is cloning property Select the desired property and click on the button named Clone Type the name you have chosen The new property keeps the values 3 3 2 3 Find make a request The find tool is in the Edit menu Make a graph with several nodes Change some properties of node for making operations Select nodes check the Filter box and select the properties you want to change viewRotation Click on the Set all button and type a value 20 for example Now you have some node with a rotation of 0 degree and some other rotated of 20 So in the Find box e Select the property used for the request viewRotation e Choose the operation and type a value for the comparaisons and 20 to find the element rotated of 20 degrees e Select the action in the Options part Add and the kind of the elements of the request on nodes 3 4 Hierarchy Tulip provides a system for the management of graphs hierarchies The hierarchy sub window displays the existing instances of subgraphs or groups with their relationships the user can change the current view of the graph by clicking directly on the tree When clicking the right mouse button a pop up menu is displayed it allows to manage the instances of cluster remove clone create subgraph 3 4 1 Definitions 3 4 1 1 Subgraphs A graph can have several parts of itself these are stored in the subgraph instances Some clustering
56. stem the root 1s the directory you have selected e GML import create a graph from this other format e dot create a graph from graphviz format The second possibility is to generate automatically different kinds of graph Graph Tree Grid which could be complete simple uniform Examples of generation e Complete General Graph e Complete Tree e Grid e Grid approximation e Random General Graph e Random Simple Graph e Uniform Random Binary Tree http en wikipedia org wiki Adjacency_matrix 16 Func tion al ties It is posssible to do a Copy Paste You can cut copy and paste selected elements from a view When you paste an element it is placed at the same location it was in the original view Use View gt Center View Ctrl Shift C to make it visible in the second view The menus and the mouse toolbar allow you to select the operation you want to perform on the selection 3 1 1 The Find tool In the Edit menu it exists a Find item allowing to do some requests on the current graph The tool gives a way to choose the desired property and the action you want perform regarding the current selection Make out of the found elements a new selection Add them to the selection Remove them from the selection or Intersect them with the current selection 3 2 Algorithms Each graph can be modified with algorithms for the layout the set of selected elements the size of nodes the value attributed to an
57. sult with our base tree and the three metrics mentionned in the introduction Figure 4 5 Scatter plot generated from the three metrics 79 As a conclusion to this first part you have learnt how to generate a simple frequency histogram from a graph and a metric You have also learnt how to generate a whole scatter plot from 2 to 3 metrics In the next part you will learn how to display the basic statical values on the graph 4 4 3 Statistics values and Augmented displays Now we will see how to compute the main statistics results and how to display them on the generated Histogram Scatter Plot Switch to the Display tab of the statistics panel Yet everything is grayed To compute the values of the tab you must click on the bottom button Compute Results Note that this button is reachable on every tab on the panel but you will be able to click it only if the Used Metrics list of the Computation tab is not empty Figure 4 6 Click on the button Compute Result to enable the tab u Tl _als Results Average M 0 Wanance 1 thi 1 Standard Deviation sigma U Bounds hin lt 0 Max 0 near Regression Function 2 metrics Ordinate in the beginning Slope Eigen Vectors 3 metrics vl 0 0 04 vi 0 0 vi 0 0 Once the results computed most of the elements of the panel should be enabled Note that the Regression Function group is enabled only if you has
58. t Wikipedia Simple graphs eAcyclic A graphis acyclic if it contains no cycle A cycle is a path that as the same source and target For more information please visit Wikipedia Acyclic graphs eConnected A graph is called connected if every pair of vertices in the graph is connected For more information please visit Wikipedia Connectivity gt eBi connected A connected graph is biconnected if the removal of any single node and his out edges can not disconnect the graph For more information please visit Wikipedia Biconnected Graphs eTri connected If itis always possible to establish a path from any node to an other one even after removing any 2 nodes then the graph is said to be Tri connected For more information please visit Wikipedia k connected graphs T http en wikipedia org wiki Simple_graph Simple_graph 2 http en wikipedia org wiki Directed_tree 3 http en wikipedia org wiki Free_tree 4 http en wikipedia org wiki Acyclic_Graph 5 http en wikipedia org wiki Connected_graph 6 http en wikipedia org wiki Biconnected_graph 1 http en wikipedia org wiki K connected_graph 3 ePlanar A graph is said to be planar if it can be drawn on the Euclidean plane without any edges crossing Wikipedia Planar Graphs eModify Those operations will modify the entire structure of a graph eMake Simple This algorithm will change the graph to make it a simple graph For more information please visit
59. te tlp gz 62 gu _als George G Robertson gt i ge F Be Ordered and qua g i ds Y w S N j 7 ON 7 tk orn 7 i T Galaxy e N 4 G 7 hi Go deeper We then select the menu item Algorithm gt Selection gt Reachable Sub Graph type 1 for the dis tance into the popup panel and O for the direction of the edges outgoing We then select the menu item Edit gt Create Subgraph to save this selection for further manipulation naming it GR 1hop outgoing We then select this new subgraph in the hierarchy tab and lay out this subgraph using a hierarchical drawing algorithm Algorithm gt Layout gt Hierarchical gt Hierarchical graph We can see simply from the drawing which papers were published first as they are cited by the later ones Robertson has published 11 papers in this database The coloring by the number of citations Algorithm gt Color gt Metric Mapping with field property set to arityOut shows that Cone Trees is his most influential work Finally we select all papers by hitting Ctrl F for the find tool choosing the type property the filter and the value O for papers We explicitly add Robertson to the selection using the selection tool to select its edges too see below and save this whole set to a new subgraph that we name GRCitesub Modeling the mighty maple ation vgealization of multivariate Yata from bic l Lab NN mr 2 anized formation of topblogically c Kobsa
60. th depth of a node or an edge To re size an edge the parameter Size Interpolation CONTROL R must be switched off For an edge the three fields are Width at source of the edge Width at the end of the edge Size of the arrow eviewTexture Texture will replace the color background of the node doxygen allPlugins html QuotientClustering 45 http en wikipedia org wiki Small world_network A off doxygen allPlugins html StrengthClustering 44 Func tion al 15 ties 3 3 2 Using Properties 3 3 2 1 Updates of property values As it is explained in the last section it 1s possible to update the properties attached to the graph elements with algorithms An other solution is to update the values through the Property tab of the Info Editor subwindow To give an example create a graph e Select the property you want to update viewSize in the Local table for example to manage the size of the nodes Now you can change all values or the value of one node 1 Click on Set all and write the new coordinates 2 0 2 0 2 0 2 Click on the line and the second column of the choosed node in the table Change the values for the width the height and depth If you want to change properties of selected elements use the check box selected only of the Property tab e Select elements with the mouse toolbar operation or using the Add Remove Selection item displayed in the contextual pop up menu which appears when pr
61. ur graph without the plug in directory To delete 1t we have first to select it and then select all its sub directories e Select the plug in directory Use the Find tool Edit gt Find or Ctrl F with the field Input property set to name filter function set to and filter value set to plugins e Select all its sub directories Use the Algorithm gt Selection gt Reachable Sub Graph algorithm with the field distance set to 50 e Delete all the selection press Del e Re draw the bubble layout Algorithm gt Layout gt Tree gt Bubble Tree Following 1s what you should see 55 As you can see the bubble tree layout can be quite useful 4 2 3 2 The Tree Map layout This Layout algorithm can be found in the menu Algorithm gt Layout gt Tree The treemap layout is very useful to notice large disk usage files This section will show you how to use the tree map layout First make sure that you have unchecked the Force Ratio option that you can access via the menu Options Apply the layout algorithm Algorithm gt Layout gt Tree gt Squarified Tree Map with the following parameters e Metric set to size e Aspect Ratio set to 1 e Texture checked Do not forget to refresh the views Ctrl Shift R Following is what you should see LELE val a BNI le d HEE mg I AE aa Y FB Tre a H H A ae 1 i As you can see we easily get a global information on the size of fi
62. we can see the labels If you want to display the big file high disc space with big nodes use the Algorithm gt Size gt Metric Mapping algorithm with the parameter called property set to size 4 2 5 Showing a specific kind of file Now that our graph as a nice and clear layout we would like to locate all of our Source files cpp To do so we will use the Find tool Edit gt Find or Ctrl F Use the following parameters e Input Property name n_n e Filter filter function set to and filter value set to cpp or hpp For more details on regular expressions follow this link WikiPedia Regex e Options check the Replace radio button and select On nodes Now that our source files are selected we will apply a different color to them In the info editor window select the node property called viewColor check the selected only option Now that we only see the viewColor property of the selected nodes click on the button Set all and choose the color that you want We choosed green You should see a graph like the one following 3 http en wikipedia org wiki Regular_expression 60 4 2 6 Conclusion As you could have seen tulip implements powerful layouts and tools to make a simple and understandable graph from a complex one 61 gu rl als 4 3 People in InfoVis 4 3 1 Analyzing an author Before anything download and open this tulip graph file Click on the tab Hierar

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