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1. paths of length exactly equal to Steps Output file name for TI matrix optional Set the name of a CSV file in which the TI matrix will be saved TO Threshold Set the threshold value for TO calculation If set to 0 the index is not calculated 4 7 Status s Contrastatus s Netstatus A s The status of node i s in a DAG is the sum of distance from node i to all others The contra status s is the same if we reverse the direction of all edges in the network Net status As equals As s s 4 We calculate these indices based on distance shortest paths however maximal and average path lengths are also possible These indices can be calculated only for DAGs i e hierarchies 4 8 K Index The keystone index K 6 is an ecological adaptation of net status intro duced in sociometry 4 and used also in ecology 5 It can be calculated for DAGs where each link connects a superior to a subordinate The keystone index of node i K is defined as Ke Keg tae Kamri hina gt zU F y qe Ke c 1 e 1 8 where n is the number of subordinates of node 2 d is the number of supe riors of its cth subordinate and K is the bottom up keystone index of the subordinate Symmetrically m is the number of superiors to subordi nate i fe is the number of subordinates of its et superior and Ke is the top down keystone index of the e superior For node i the first sum in the equation i e X 1 de 1 Ke2. us library ms 141122 aspx An interesting feature of the visualization toolkit 1s to use pictures for representing graph nodes e g a lion It can be used for educa tion purposes or just simply to improve the didactics of professional presentations Pay attention to letter case of properties and graphical attribute they are case sensitive That means for example that Label with capital L is different than label with small 1 17 Name Label Color BorderColor BorderSize Width Height GraphicElement GraphicElementFile Description Set a string that will appear over a node Set the fill color of a node Set the outline color of a node Set the thickness of the node outline Set the width of a node Set the height of a node Set the node aspect Set the node aspect Accepted values any value names of colors or numbers between 0 and 100 that will be represented as a gray scale names of colors any number numbers greater than 20 numbers greater than 20 a string containing XAML code a path of a file which con tains XAML code Table 2 Graphical attributes of a node Name Label Color Stroke Thickness Description Set a string that will appear over an edge Set the color of an edge Set the thickness of an edge Accepted values any value names of colors or numbers between 0 and 100 that will be represented as a gray scale any number Tabl
3. Lo W T Cheng l J and Lee L H A trophic model for kuosheng bay in northern taiwan J Mar Sci Technol 12 424 442 2004 Fruchterman T and Reingold E Graph drawing by force directed place ment Software Practice and Experience 21 1129 1164 1991 Brandes U A faster algorithm for betweenness centrality Journal of Mathematical Sociology 25 163 177 2001 Duncan J Watts and S H Strogatz Collective dynamics of small world networks Nature 393 440 442 1998
4. The Microsoft Research University of Trento Centre for Computational and Systems Biology Q aid ne 41010010 010100101 01101101010 CosBilLab Graph User Manual The Microsoft Research University of Trento Centre for Computational and Systems Biology graph cosbi eu Version 1 0 Date 06 11 2009 You may use copy reproduce and distribute this software for any non commercial purpose subject to the restrictions in CoSBi SSLA This software comes as is with no warranties This means no express implied or statu tory warranty including without limitation warranties of merchantability or fitness for a particular purpose any warranty against interference with your enjoyment of the software or any warranty of title or noninfringement There is no warranty that this software will fulfill any of your particular purposes or needs Also you must pass this disclaimer on whenever you distribute the software or derivative works Contents 1 1 Welcome to CoSBiLab Graph TEE ETT rro oriol 14 Download sra wea te dw ee he ewe Ew we Ewe PR 34358 ne ee h wee eee ee eee Eee 2 1 Create the first graph 0 0 2 00008 aaa Pee eae ee panes ee ee RA AAA 2 0 Group nodes 2 a 2 6 Import data from Beta Workbench 2 3 Layout TETERA CENA AAA arar ee A ee 4 4 Betweenness Centrality 4 5 Clustering Coef iciembl
5. a force directed layout any Cek y ES o Reingold TAL Grid Draw nodes on the intersections any of a grid H sinuisoid Draw nodes along a sinusoidal any line V sinuisoid Draw nodes along a sinusoidal any SN TAZA Ah line rotated by 90 degrees W AR Spiral Draw nodes along a spiral line any es see Name Description Type Example Circle Draw nodes on a circonference any AA ae A o Table 1 List of layouts Part of the algorithms derives from NodeXL http www codeplex com NodeXL It is a comfortable and user friendly property of the software com pared to several other similar softwares that rearrangements in graph layout can be saved F igure 5p shows our food web with a random lay out and F igure 5p shows nodes rearranged according to trophic levels plants are at the bottom and top predators are at the top This can be saved and new work can be started from here 4 Actions The actions menu offers all the operations and measures computable for the selected graph Here we provide additional topological indices for network nodes quantifying various aspects of their indirect neighbourhood in the graph i e characterizing their network position in a more sophisticated way The menu items with suspension points need some parameters In this sec tion is gave an overview about the available algorithms Some of the actions have a huge computational cost so run them without tune the p
6. arameters or over big graph can freeze the applica tion for a long time 4 1 General Informations Graph Statistics print into the console the kind of graph not directed di rected with cycles DAG rooted DAG forest or tree and the number of nodes and edges 4 2 Components This algorithm count the number of components in the selected graph A component is a subgraph in which any two nodes are connected to each other by at least a path When ColorComponents parameter is checked each component will assume a different color 4 3 Degree Degree counts the number of incoming InDegree ougoing OutDegree and adjacent links Degree for each node The last measure is calulated as D Dna F Donto In case of undirected graph only the number of adjacent links is reported 4 4 Betweenness Centrality Betweenness coefficient quantify the centrality of a node according to the ratio between the number of shortest path passing through that node and the total number of shortest path 1 Its formulation is Calo Y Talv O st sAvAteV s t where os is the number of shortest path between node s and node t and Os uv is the number of shortest path between node s and node t passing through v The measure is calculated through the Brandes algorithm 12 4 5 Clustering Coefficient The clustering coefficient of a graph node quantifies how densely its neigh bours are connected to each other In other words it is the number of l
7. c quantifies the bottom up effect Kou while the second sum i e gt 1 f 1 Kie quantifies the top down effect Kiai After rearranging the equation terms including Ky and Kie i e Y Kec de gt gt Kte fe refer to indirect effects for node i Kinair while terms not containing Kp and Kie i e gt 1 d 5 1 fe refer to direct ones Kairi Both Mine Kiai and Kindiri Kairi equals K 13 K quantifies only vertical indirect relationships but characterises posi tional importance by separating indirect from direct as well as bottom up from top down effects in the network Its important feature is the sensitivity to both distance and degree it quantifies meso scale network position 7 These indices can be calculated only for DAGs i e hierarchies 4 9 Cycles This algorithm calculate the number of different cycles belonging to the graph It can also enumerate them and save the list in a CSV file The number of cycles is displayed after the execution in the console The param eters are Threshold Set the maximum length for recognized cycles When its value is set to 0 means that there is no limitation When this algorithm is executed over a huge graph is recommendable set a threshold different than 0 OutputFile optional Set the path of an output file where all the cycles detected are listed AllowVerticesRepetition When checked means that a cycle can pass in finity times by the same node When checked thresh
8. e 3 Graphical attributes of an edge 18 Figure 7 Indexes represented by size and color the size of the nodes is proportional to TI index and the darkness with K References 1 Freeman L C A set of measures of centrality based on betweenness 12 13 _ LL Sociometry 40 35 41 1977 Lorenzo Dematt Corrado Priami and Alessandro Romanel The beta workbench a computational tool to study the dynamics of biological systems Briefings in Bioinformatics 9 437 449 2008 Lorenzo Dematt Corrado Priami and Alessandro Romanel The blenx language A tutorial In LNCS editor SFM 2008 pages 313 365 Springer Verlag 2008 Harary F Status and contrastatus Sociometry 22 23 43 1959 Harary F A structural analysis of the situation in the middle east in 1956 The Journal of Conflict Resolution 5 167 178 1961 Jordan F Takacs Santa A and Molnar I A reliability theoretical quest for keystones Oikos 86 453 462 1999 Jordan F and Scheuring I Searching for keystones in ecological networks Oikos 99 607 612 2002 Jordan F Liu W C and Mike A Trophic field overlap a new approach to quantify keystone species Ecological Modelling 220 2899 2907 2009 Jordan F Liu W C and van Veen F J F Quantifying the impor tance of species and their interactions in a host parasitoid community Community Ecology 4 79 88 2003 Lin H J Shao K T Hwang J S
9. e different formats including outputs from the BlenX environment DOT and DIP Imported network data can be changed by adding or removing nodes Graph descriptor files supported by Graphviz http graphviz org DL files are supported by UciNET http www analytictech com We will illustrate the most important features of the software by the example of the Kuosheng Bay food web 10 already analysed topo logically im details 8 So this network of 15 nodes may be regarded as our real toy model 2 1 Create the first graph Start CoSBiLab Graph and select File New Graph from the menu or click on the New icon showed in the tool bar A new window appears to choose the kind of graph you are interested in By default you can choose only between directed and undirected graph Click for instance on Undi rected graph The main part of the window is now representing a new empty graph called Graph 1 The insert icon is selected in the Tools tool bar which means that is possible to add new nodes and links You can choose the kind of item that you want to add to the graph in the Items Palette docked window By default a node is selected By clicking on the graph area a new node is added At each new click a new node is added To add an edge select the edge item from the Items Palette then press the left button of the mouse over one node in the graph Keeping the button pressed move the cursor over another n
10. eee LO Ni A A AAA aa aaa 4 7 Status s Contrastatus s Netstatus A s A WINGER ARS 4 9 Cycles 4 10 Cycle Sign 4 11 Shortest Path Matrix 4 12 Export graph to image 5 Advanced Topics 5 1 Add Expressions to all nodes or all edges 5 2 Bind properties with graphical attributes 10 10 10 10 10 11 11 12 13 13 14 14 15 15 1 Introduction 1 1 Welcome to CoSBiLab Graph CoSBiLab Graph can construct visualize and modify graphs as well as cal culate measures and layouts CoSBiLab Graph can import and export data in a variety of formats among which the reaction network generated by the Beta Workbench 1 2 License CoSBiLab Graph is a free downloadable application for non commercial purposes covered by the Microsoft Research University of Trento Cen tre for Computational and Systems Biology Shared Source license agreement CoSBi SSLA 1 3 System requirements Microsoft NET Framework 3 5 SP1 1 4 Download CoSBiLab Graph is freely downloadable for non commercial purposes at www cosbi eu 1 5 Support CoSBi is very interested in your opinion If you want to report issues give feedback or ask a question send a mail to graphQcosbi eu 2 Getting Started Basically there are two options how to start network analysis creating a graph File New graph see details in 2 1 or importing graph data File Open Importing data is possible in fiv
11. ffects through n steps are considered we define the effect received by node i from all other nodes in the same network as Vas Ur Me 1 J which is equal to 1 i e each node is affected by the same unit effect Furthermore we define the n step effect originated from node i as Me Oni y On ji 1 J that does vary among different nodes i e effects originated from different nodes are generally different Here we define the TI centrality TI stands for topological importance of node i when effects up to n steps are con sidered as N Xma Imi _ Demat 231 msi n n TI 2 11 that is simply the sum of effects originated from node i up to n steps averaged over by the maximum number of steps considered n For weighted networks all effects are defined in the same way as above but 1 step effects are Es ee Hi where u is the sum of link weights adjacent to i ande is the weight of the link between i and j Furthermore we define WI as the topological importance of node i in weighted networks when effects up to n steps are considered N Xma Imi L om Ziz Ami n n WE 2 4 6 2 TO WO TI and WI quantifies the relationship between every pairs of nodes in a connected network if n is large enough everything is connected to everything else directly or through indirect pathways To measure the uniqueness of the position of a netw
12. hen the Select tool is selected point the mouse over the graph and rotate the wheel of the mouse to zoom Finally you can also press Ctrl and select an area of the graph by keeping pressed the left button of the mouse to zoom in 2 4 Items palette The Items palette allows to choose the type of item that will be inserted during the nexts insertion in the graph Each time that a new item is selected the Insert Tool is selected so the application is ready to insert that item inside the selected graph The items inside the items palette depends by the graph template selected when the graph was created 2 5 Group nodes CoSBiLab Graph can select a group of nodes and collapse them in a single node which mantains the same edges with neighbor nodes To group nodes click on the group icon in the tool bar or select Group from the Tools menu Items Palette Figure 3 The items palette Figure 4 The Kuosheng Bay network before a and after b aggregating red nodes the aggregate is the black node Move the cursor over the graph press the left button of the mouse and by keeping it pressed move the cursor in order to select an area The nodes inside the selected area will be collapsed into a single node When nodes are grouped the active tool becomes Select so that to group other nodes you have to select again the group tool from the tool bar Nodes co
13. inks between its neighbours divided by the maximum number of links between them It can be averaged over the whole graph if one wants to provide a global network measure see 13 10 4 6 TIWI The following indices characterize network position in any graphs The first indices are centrality measures in binary 7 1 and weighted W I networks 9 while the indices in the second group are the derived redundancy indices in binary TO and weighted WO networks 8 4 6 1 TI WI We assume a network with undirected links where effects can spread in any directions We first consider unweighted networks Here we define a j as the effect of j on i when i can be reached from j in n steps The simplest mode of calculating ani is when n 1 i e the effect of j on i in 1 step di 1 Di where Di is the degree of node i We assume that indirect effects are multiplicative and additive For instance we wish to determine the effect of j on i in 2 steps and there are two such 2 step pathways from j to i one is through k and the other is through h The effects of j on 1 through k is defined as the product of two direct effects i e G14 X aiik therefore the term multiplicative Similarly the effect of j on i through h equals to 1nj1X 1in To determine the the 2 step effect of j on i a2 we simply sum up those two individual 2 step effects i e a2ij G14 X Qik Ginj X Ain and therefore the term additive When e
14. llapsed together can be expanded by right clicking and choosing from the contextual menu the Expand group item The information regarding the nodes contained inside a cluster node are temporal and are not saved to a file Figure 4 shows the original Kuosheng Bay network Figure 4a and the same network after aggregating herbivorous zooplankton and carnivorous zooplankton in red Figure 4b Poperties inspector tells how many nodes have been aggregated into particular components For the aggregates topo logical indices can be calculated again after aggregation 2 6 Import data from Beta Workbench With CoSBiLab Graph you can extract from a simulation output file spec the reaction graph Click on Open icon or select Open from File menu Now select BlenX spec files from the file extension combo box at the bottom of the open dialog Select a spec file and click Open button The imported graph represent each reaction as a gray node and each reac tants as a colored node with a size proportional to the number of reaction in which it is involved Another graph generated by the BetaWB is the CTMC which represent the state space of a BlenX program A Dot file is generated by running the simulator with parameter r SBML BetaWB is a collection of tools based on the programming language BlenX explicitly designed to represent biological entities and their in teractions The BetaWB includes the BetaWB simulator a stochas tic simulator based o
15. n an efficient variant of the Gillespie Stochas tic Simulation Algorithm SSA the BetaWB designer a graphical editor for developing models and the BetaWB plotter a tool to an alyze the results of a stochastic simulation run For more informa tion please visit http www cosbi eu index php research prototypes beta wb 3 Layout CoSBiLab Graph implements many layout algorithms to draw a graph You can choose a layout by selecting an item from the Layout menu Note that some of them cannot be applied to every graph For example Balloon tree layout can be applied only to directed acyclic graph When the selected algorithm is not applicable an error message is shown on the console Figure 5 The Kuosheng Bay network in random layout a and a manually rearranged saveable form where plants are at the bottom and top predators are at the top b In the latter all links point upwards Name Description Type Example a Random Draw the nodes in a random po any i HIS ANY ARS EJ NO ADRIAN NA o N WHAT A a RMD Pa i A SOY a sition LN dant E PIRK A x gt 1D NN E l he Let See op Balloon Draw the network according to DAG Z tree the graph hierarchy putting the l parent at the centre of a circle of children Tree Draw the graph according its hi Tree e E erarchy putting the children be low the parent Name Description Type Example Fruchterman Is
16. nding has no effect Let s introduce an example You can bind a property called attributel with the graphical attribute Width by appending the string attributel Width to the VertexViewBinder If none of your nodes has a property called at tributel you will not note any difference Now select a node and through the Properties Inspector add a new Property called attributel of type String and with value 40 As soon as you click on the Add button the selected node will double its width If you try to play a bit with the value of attributel you will note that at each change in the value of attributel the size of the node is modified Now try to change the value of attributel to red The width of the node is reset to its default value because the system cannot bind a string value like red to a numeric attribute like Width Same thing happen when the value is out of range as setting a value less than 20 for attributel In another example figure 7 is showed how the graphical attributes are used at the same time to represent different indexes in particular the size of the nodes is proportional to TI index and the color with K Table 2 contains all the graphical attributes that can be set for a node Table 3 contains all the graphical attributes that can be set for an edge XAML is a declarative XML based language which is used to initialize structured values and objects For more informa tion please visit http msdn microsoft com en
17. ode of the graph and release the button The graph can be saved by clicking on the Save icon or selecting File Save from the menu 2 2 Properties Inspector The Properties Inspector docked window shows the properties of the selected item and allows you to add remove or modify properties A property is any data identify by a unique name inside the item When performing calcula tions on the network see 4 certain outputs node properties will become automatically available in the Properties Inspector panel Then these node characteristics can be used for example for visualisation see 5 2 The data inside the Properties Inspector are referred to the selected item which can be a node an edge or the whole graph In order to select a new item click on the Select icon into the toolbar or select Tools Select from the menu Move the cursor over a node an edge or the background area for the whole graph and click Now the Properties Inspector appears like in figure 1 At the top of the window is showed the kind of object selected The main part of Properties Inspector E Graph Mame Value Name Graph 1 Id 104 Id 94 Is Directed Location 370 274 Is Directed Node 2 N Edges 7 blue VertexViewBinder label Label EdgeViewBinder label Label Figure 1 The Properties Inspector showing properties of a graph a a node b and an edge c the inspector contains a list of property names and
18. old must be set different than 0 4 10 Cycle Sign This algorithm similarly to the cycles algorithm enumerate all the cycles in a graph and for each of them calculate a sign At the end of the execution a summary table will appears into the console For each cycle length there is a row with the length the number of cycles of that length percentage of positive and negative cycles mean weight mean weight in positive loops and mean weight in negative loops The parameters are SignAttribute Set the name of the sign attribute in the edges It can bea number or a string which assume values or If an edge don t have this attribute plus sign is assumed by default Weight Attribute optional Set the name of the weight attribute in the edges This attribute can assume numeric values If an edge don t have this attribute a value of 1 is assumed by default 14 Threshold Set the maximum length for recognized cycles When its value is set to 0 means that there is no limitation When this algorithm is executed over a huge graph is recommendable set a threshold different than 0 OutputFile optional Set the path of an output file where all the cycles detected are listed with their sign and weight AllowVerticesRepetition When checked means that a cycle can pass in finity times by the same node When checked threshold must be set different than 0 The ratio of negative cycles to total cycles provides a measure of str
19. ork node to what extent its neighbourhood overlaps with that of others we define an effect threshold t determining the effective range of the interaction structure of node i We regard nodes within this effective range as strong interactors the effects they receive from node i is larger than t while nodes outside this range are weak interactors Sets of strong interactors of two nodes i and j may overlap The topological overlap T O between nodes i and j is the number of strong interactors appearing in both 1 s and j s effective ranges as a function of maximal step number n and threshold t The sum of all TO values between node i and other nodes C TO summed over all j with 4 j provides the summed topological overlap of species i TO The output of computing the above indices is four matrices for pairwise TI WI TO and WO relationships among nodes and four vectors for nodal sums Beyond the exported outputs the software shows these summed nodal parameters in Properties Inspector The parameters are Weight attribute name optional Set the name of an attribute which indicate the weight of the edge If the attribute is not present has an invalid value or this parameter is not set the weight value is set to 1 by default Steps Indicates the number of steps for the index 12 Compute Up To Step values When checked compute the index consid ering paths of length less or equal to Steps otherwise considering
20. tead of a number you can put the name of a property belonging to a node edge e g value 10 5 If the expres sion is correct it will have a yellow background otherwise red When the expression is ready click apply to copy and evaluate it in each node edge If the expression cannot be evaluated in a node or in an edge because the properties used inside the expression are not present or because their values are not numbers the expression appears as its formulation surrounded by square parenthesis otherwise appears its evaluation Note that if the expres sion cannot be evaluated due to values out of expected range e g sqrt 5 the evaluation will be NaN that means not a number 5 2 Bind properties with graphical attributes The graph visualization can become a lot more intuitive and expressive if properties belonging to nodes and edges are represented through graphical attributes like color size etc CoSBiLab Graph allows you to do it easily With the Select tool activated click on an empty area of the graph in order to visualize the graph properties inside the Properties Inspector You can note two properties named VertexViewBinder and EdgeViewBinder These 16 two properties are lists of element of the format PropertyN ame Graphical Attribute Each of these elements bind a property to a graphical element The type and the value of the property must be compatible with the graphical attribute otherwise the bi
21. uctural balance 5 4 11 Shortest Path Matrix Computes the shortest path for each pair of nodes and print the results in a matrix When there are no path between two nodes the distance is set to 0 The parameters are Inverse Path When checked in a directed graph compute the shortest path walking through the edges in the opposite direction Weight attribute optional Specify a name of an edge attribute which represent the wheight Output File Name Specify a name for a CSV file in which the resulting matrix will be printed 4 12 Export graph to image Export to a PNG file the current view of the selected graph The parameters are File Name Specify the output file name DPI Specify the Dot Per Inch resolution of the output file 15 Insert the expression name El Insert the expression El Strin Expression Apply Cancel Apply Cancel Figure 6 Add expression windows 5 Advanced Topics 5 1 Add Expressions to all nodes or all edges You can add a mathematical expression to all nodes or all edges by selecting Add expression to all nodes or Add expression to all edges from the Graph menu In the input box type a name to identify the new expression then click the apply button At this point a new input box in which you can spec ify the expression appears The expression can be composed by numbers arithmetical operators parenthesis and the mathematical functions pow base exp and sqrt number Ins
22. values The background colour of the fields gives you important information about the value Gray The value is not editable White The value can be edited Yellow The value was just modified Red The value that you have typed in is not valid and will not be saved The tool tip which appears by moving the cursor over a value suggests the type of data At the bottom of the Properties Inspector there are two buttons The red X remove the selected property if it is not read only The green plus add a new property and if clicked it change the aspect of the Properties Inspector like in figure 2 From there you can choose a name a type and a value for the new property then click again to confirm the addition of the property or click the red X to cancel the operation 2 3 Navigator The navigator component shows a map of the entire graph A dark blue rectangle represent the portion of the graph visualized inside the graph win dow The navigator is entirely blue if the complete graph area is visible Ala Vertex New Attribute Attribute Name value Attribute Type string String Floating point Number Attribute Value aE ds Figure 2 Add a new property inside the window By clicking on the map you can move the visualized area to another part of the graph At the top of the Navigator there are three buttons Zoom out Original size and Zoom in which modify the scale rate of the view Alternatively w
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