Exploring social structure using dynamic three
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1. 10 step geodesic cycle This cycle is shown alone in the second image When examining the various images readers should also examine the ID number for informa tion on the road upon which the person lives and on pairs linked by sibling ties Long cycles of this sort are practically never seen in networks of personal affiliation Freeman then sent the first image to Kirke and asked if she had any ideas about how it happened to be found in her data She replied immediately and she came up with a number of ideas that were suggested to her by looking at the image In the first place Kirke indicated that contrary to 7 Tt should be noted that there is a missing line in this diagram the wavy line depicting a sibling tie between 014912 to 014914 at the upper right of the figure was omitted 8 Run MAGE Click on Proceed Pull down the File menu hit Open file and open the file kirke kin Open the image by clicking your cursor over the black window You can move from image to image by clicking repeatedly on the ANIMATE button on the right of the screen To determine the identity of any individual simply put the cursor over that individual and hit its primary key Kirke s ID number for that person will appear at the lower left corner of the screen The decimal number that appears above the label is the Euclidean distance of that point from the one previously chosen 116 L C Freeman et al Social Networks 20 1998 109 12. Next to explore the mutual Best Friends ties or select Choose and type in 3 to examine the Close Friends Both images begin with the same initial orientation as in the first image The simplest way to progress through the various options provided is to hit the ANIMATE button on the right The actors are shown in yellow with the Best Friend ties in pinktint and the Close Friend ties in bluetint To continue hit the ANIMATE button again and the image will jump to reveal in which of the two wings these best or close friends are located Hit the ANIMATE button again and those best or close friends both living in Wing A A A Ties are displayed Since there are multiple floors on each wing we can investigate which best or close friends live on the same floor in bluetint and which live on different floors in darker blue but also in Wing A The B B Ties show those living in Wing B also shown are those on the same floor in green and those on different floors in cyan but still in Wing B A B Ties are those best or close friends who live in different wings Continue to hit the ANIMATE button to reveal those best or close friends who are of the same sex F F Ties or M M Ties and those who are of the opposite sex F M Ties Similarly you can highlight those who are in the same year 1 1 Ties or 2 2 Ties and those who are in different years 1 2 Ties As would be expected the g
3. SOCIAL NETWORKS ELSEVIER Social Networks 20 1998 109 118 Exploring social structure using dynamic three dimensional color images Linton C Freeman Cynthia M Webster Deirdre M Kirke School of Social Sciences University of California Irvine CA 92697 5100 USA 8 Department of Anthropology and Sociology University of Queensland Brisbane QLD 4072 Australia Department of Sociology National University of Ireland Maynooth Kildare Ireland Abstract Here we introduce a computer based visual display program called MAGE MAGE was designed to display molecules but we will explore its potential for application to the study of social networks To do so we will use MAGE to examine the structural properties of two data sets friendship choices in an Australian college residence and peer choices among teenagers in a Dublin suburb 1998 Elsevier Science B V 1 Introduction In his recent book on microphysics Galison 1997 discussed two kinds of instru ment builders in that field There are those who build graphic devices that produce visual images of particular particle interactions and there are those who build computa tional devices that are designed to analyze vast amounts of data on such interactions A similar division between visual and computational instruments can be found in social network analysis We use tools like KrackPlot Krackhardt et al 1995 that produce pictures of the
4. 523 534 Priest R F Sawyer J 1967 Proximity and peership bases of balance in interpersonal attraction Am J Sociol 72 633 649 Richardson D C Richardson J S 1992 The Kinmage a tool for scientific communication Protein Sci 1 3 9 Romney A K Weller S C 1984 Predicting informant accuracy from patterns of recall among individuals Soc Networks 6 59 77 Webster C M 1995 Detecting context based constraints in social perception J Quant Anthropol 5 285 303 Weller S C Romney A K 1990 Metric Scaling Correspondence Analysis Sage Beverly Hills Wilkinson L 1989 SYSTAT The System for Statistics SYSTAT Chicago
5. clicking If the author has specified multiple images the user can move from image to image by pulling down the KINEMAGEB window and choosing Next or by choosing Choose and then specifying an image by number All this permits the author to pre program some of the user s experience by including text and captions and by specifying particular views of particular objects But at the same time users are completely free to interact with the pre programmed objects and to modify the views to suit themselves Such flexibility permits users to explore the data in their own ways and to arrive at their own conclusions The KIN input file for MAGE must contain a list of points as well as a location in a three dimensional x by y by z space for each point Locations can be arbitrary or they may be produced by some systematic procedure Typically points are placed by using a gravitational model Kamada and Kawai 1989 or on the basis of the results of statistical computations like multidimensional scaling Kruskal and Wish 1978 corre spondence analysis Weller and Romney 1990 or some form of cluster analysis Arabie et al 1996 To see how all this works in the social networks context we will first try using it to model a data set collected by Webster 3 The Webster data set Webster collected friendship data among the 217 residents living at a residence hall located on the Australian National University campus Residents were i
6. in the plane of the screen clockwise or counterclockwise Moving the cursor over it and clicking can pick any point in the image The screen will then display any information the author stored regarding that point name or attributes and it will show the distance of the chosen point in three space from the point previously chosen Sliders on the right edge of the main screen facilitate other user controls Users can move into an image or away from it by using the ZOOM slider The ZSLAB slider controls contrast and ZTRAN controls brightness Typically users will not need to adjust the ZSLAB or the ZTRAN slider Also on the right side of the main screen but not clear out at the edge are a series of switches defined by the author of each specific image and linked to that image These switches can be used to turn particular features of the image off or on and thereby to call attention to its various structural properties Pull down menus permit other adjustments and refinements The most useful of these menus are labeled VIEWS and KINEMAGE The user can always return to the L C Freeman et al Social Networks 20 1998 109 118 111 original view specified by the author by pulling down the VIEWS window and choosing the View 1 option If the author has specified more than one view more than one option will be highlighted and the reader can choose any one of them simply by pointing at it and
7. program to display downloaded KIN images or it can be attached to a web browser Netscape or Microsoft Internet Explorer in order to display images automatically whenever they are confronted on the web If you simply load MAGE on your MAC or PC you can run it by clicking on its icon and loading a KIN file MAGE then opens five windows 1 a large main window that contains the pull down menus and image control sliders 2 a text window 3 a caption window 4 an image window and 5 a banner window for starting the program The banner window allows you to start in the regular mode or in a limited student mode The regular start is preferred Once MAGE is started you can move among these windows either by clicking on the desired window itself or by pulling down the Windows menu and choosing Show text Show caption or Show graphics You can load a KIN data file or you can change files at any point by using the Open File command in the File pull down menu MAGE permits rotation of three dimensional objects in order to help viewers explore the details of any structure that is displayed If you place the cursor in the graphics window and hold down the primary mouse button you can rotate the image by moving the mouse Left right motion in most of the window spins the image horizontally Up down motion spins it vertically And left right motion when the cursor is in the top sixth of the window spins the image
8. social relationships in a small voluntary association J Anthropol Res 29 96 112 Feiring C Coates D 1987 Social networks and gender differences in the life space of opportunity introduction Sex Roles 17 611 620 Festinger L Schachter S Back K 1963 Social Pressures in Informal Groups a Study of Human Factors in Housing Stanford Univ Press Stanford Freeman L C 1979 Expectations in a social network the small world of Bochner Buker and McLeod revisited Connections 3 89 91 Galison P 1997 Image and Logic a Material Culture of Microphysics University of Chicago Press Chicago Ibarra H 1992 Homophily and differential returns sex differences in network structure and access in an advertising firm Adm Sci Q 37 422 447 Ibarra H 1993 Personal networks of women and minorities in management a conceptual framework Acad Manage Rev 18 56 87 Kamada T Kawai S 1989 An algorithm for drawing general undirected graphs Information Processing Lett 31 7 15 Kirke D M 1996 Collecting peer data and delineating peer networks in a complete network Soc Networks 18 333 346 Krackhardt D Blythe J McGrath C 1995 KrackPlot 3 0 User s Manual Carnegie Mellon University Pittsburgh Kruskal J B Wish M 1978 Multidimensional Scaling Sage Beverly Hills Nakao K 1987 Analyzing sociometric preferences an example of Japanese and US business groups J Soc Behav Pers 2
9. structure of a particular network and we have programs like UCINET Borgatti et al 1992 that facilitate computations on social network data The present paper is focused on an instrument of the first kind We will introduce MAGE Richardson and Richardson 1992 a computer graphic program and evaluate its potential for applications in social network analysis To conduct that evaluation we will draw upon two data sets and see what we can uncover using this strictly graphic approach Corresponding author E mail lin aris ss uci edu E mail c webster mailbox uq edu au E mail dmkirke may ie 0378 8733 98 19 00 1998 Elsevier Science B V All rights reserved PII S0378 8733 97 00016 6 110 L C Freeman et al Social Networks 20 1998 109 118 2 The MAGE program MAGE was developed as a device to be used in molecular modeling It produces three dimensional scientific illustrations that are presented as interactive computer displays Transformations of these displays are immediate Images can be rotated in real time parts of displays can be turned on or off points can be identified by picking them and changes between different arrangements of objects can be animated MAGE has been compiled on and will run on PCs under Windows 3 1 3 11 95 NT or Linux MACs and on most common UNIX based workstations It displays images of files that have been prepared in a format called KIN MAGE can either be run as a stand alone
10. union of all these relations and defined that as a peer relation She partitioned the data into weak components distinct collections of teenagers who were linked together by chains of these relations but not linked to outsiders The largest of these components contained 26 teenagers She illustrated the patterning of the peer relations linking these 26 along with sibling ties in her Fig 2 reproduced as Fig 2 here 7 A six digit identification is given for each member of the network The first two digits indicate the road on which the person lives The next three digits are the family s number These numbers are assigned consecutively along the road The final digit is the identification number of a particular individual in that family When Fig 2 was originally published Freeman studied it but was unable to uncover much structural information from his inspection So he coded the data from the figure as a symmetric matrix and calculated the graph theoretic distance between all pairs of individuals He entered that distance matrix into the UCINET multidimensional scaling program Borgatti et al 1992 and solved in three dimensions where stress was less than 0 002 He then placed the points in three dimensional space and redrew the graph The three dimensional image is presented as the opening image when the file kirke kin is loaded into the MAGE program The first image presented by MAGE is striking because it contains a very long
11. 18 Fig 2 Ties linking teenagers in Kirke s largest component straight lines are peer ties wavy lines link siblings Freeman s assumption the sibling relation was distinct it was not part of her defined peer relation So Freeman separated the sibling from the peer ties in the image The third MAGE image shows only the sibling pairs And in this image we can see two things 1 there are relatively few sibling links compared to the number of peer links in this structure and 2 these sibling links may have a key role in producing the cycle The fourth image shows only those ties that were based on the peer relation And it is clear when we examine that image that removal of the sibling link at the top of the page eliminates the cycle Kirke went on to suggest that there is more to the story however She pointed out that the graph contains 17 males and nine females and that the males were generally connected to males and the females generally connected to females The exceptions she said were three in number One 15 year old male 015211 who mentioned an 18 year old female who lives on the same road 015141 as a pal but was not mentioned in return One 18 year old male 054491 mentioned an 18 year old female who lives on the same road 054451 also as a pal again without being mentioned in return And the third male female link is the sibling link between a female 015121 and her brother 015122 This suggested th
12. at it would be useful to distinguish between males and females In the fifth image females are shown in red and males in green Peer ties are gold and sibling ties are blue And as the image shows it is the brother sister tie between L C Freeman et al Social Networks 20 1998 109 118 117 015122 and 015121 that completes the cycle So the tie that completes the cycle is not only a sibling tie it is the only cross sex sibling tie What the structure seems to indicate is that in suburban Dublin teenagers of this age 14 through 18 years form their peer ties overwhelmingly with others of the same sex Some pal ties were formed between males and females living on the same road but this was not a general pattern It may be important to the formation of boy girlfriend relationships in the near future Moreover cross sex siblings may be crucial in linking their same sex friends to young people of the opposite sex It seemed reasonable then to re analyze the data taking the peer relation alone So we removed the sibling ties recalculated graph theoretic distances and re scaled the data The result is shown in the sixth MAGE image By rotating this new image new insights are generated It becomes clear that these boys and girls pattern their friendships in very different ways The boys seem to get organized into two rather tight knit little clusters in which each is tie to most of the others and the clusters are linked by a 14
13. eft Spatial proximity does seem to have some impact More residents living in Wing A in bluetint appear to be on the left side of the horizontal x dimension while more residents in Wing B in green are on the right side The vertical y dimension also shows some separation with Wing A residents towards the top and Wing B towards the bottom The third z dimension is difficult to see because it goes in and out in the image To make it clear you could spin the image further or better still you can simply pull down the VIEWS menu and choose View 2 View 2 rotates the image 90 to the right and reveals the z dimension horizontally The distinction between the wings is quite apparent from this perspective We also can look at whether the friendship structure of the residence hall is affected by interpersonal similarity The residence hall contained 104 females and 113 males In addition 91 of the 217 were first year residents All the floors on both wings housed females and males as well as some first year residents and some residents who had lived in the hall for a longer period of time Sex and Years are the two pertinent categories since all but a few of the residents were white 93 undergraduate students 95 between the ages of 18 to 22 93 To explore the effects of sex turn off the WINGS button and hit the Females and Males buttons There does not appear to be much segregation by sex In View 2 a cl
14. linked or dissimilar in their pattern of connection to others at some distance from each other 112 L C Freeman et al Social Networks 20 1998 109 118 5 4 3 O g1 Oo oH 9 First Axis Fig 1 Two dimensional plot of the first two axes of the correspondence analysis on Webster s residence data If the transformed data lack interesting structural properties if individuals are found to pair up more or less at random correspondence analysis will place the points in a roughly spherical arrangement in which those near the center will be more densely packed and those farther out will be relatively sparse But if social differentiation is present the image should display some non spherical properties Normally only two dimensions are retained from the output of correspondence analysis and they are used to generate a flat two dimensional picture The first two axes produced by the residence data are shown in Fig 1 Fig 1 typical of network graphics was produced by SYGRAPH Wilkinson 1989 It shows that these friendship data do not display a simple spherical structural form Since the data display a three pointed propeller like form some interesting structural differentiation does seem to be present Compare Fig 1 with what the correspondence analysis output produces in the way of a MAGE image The first three axes of the correspondence analysis were used to provide three dimensional locations for points The
15. nterviewed individually at the start of the university s second semester First they were asked to recall all of their friends who currently lived in the residence hall They then were provided with a list of all residents and were asked to add anyone whom they also considered a friend but had forgotten to include From the complete list of friends they were asked to indicate the strength of each friendship tie Most specified three levels of friendship best friend close friend and friend The data were combined to form a valued actor by actor matrix of reported friendship relations For the present illustrative application we began with the square non symmetric data matrix described above That matrix was first symmetrized by taking for each pair of points i j the maximum of the strengths of the two ties from i to j and from j to i Then we used the correspondence analysis routine from UCINET Borgatti et al 1992 to uncover the basic structure of the data gt The structure of KIN files is specified in detail in a text file called KinFmt31 txt This file is included in the MAGE package that can be downloaded from any of the sites listed in the Editorial on p 107 of this issue All of these computational techniques are designed one way or another to place points that are adjacent or closely linked or similar in their pattern of connection to others close together and points that are not adjacent or not closely
16. on are spatial proximity and interpersonal similarity Time and again it has been shown that individuals who live closer to one another tend to interact more frequently with one another Festinger et al 1963 Priest and Sawyer 1967 Coombs 1973 Freeman 1979 Studies conducted to identify relevant dimensions of interpersonal similarity consistently find sex and status to have an impact on behavior and perception Pairs of individuals of the same sex tend to interact more often with one another and have closer ties than do cross sex pairs Caldwell and Peplau 1982 Feiring and Coates 1987 Ibarra 1992 1993 Similarly pairs of individuals of similar status tend to interact more often with each other than do pairs who differ in status Blau and Duncan 1967 Nakao 1987 Brewer 1995 Webster 1995 Both proximity and similarity can be examined in relation to the residence data by coloring points corresponding to these features To do this it would be useful to return the image to its original x y z orientation in terms of the axes produced by the correspondence analysis Pull down the VIEWS menu and choose View 1 The residence hall is physically divided into two wings with a common ground floor connecting the wings Residents room locations can be revealed by hitting the Wing A and Wing B buttons on the right of the image To see the differentiation due to physical proximity by wings spin the image a bit to the l
17. pectives in viewing the data and to come to their own conclusions The code that produces MAGE images is simple straightforward and easy to produce and to modify It is coded in an ordinary ASCII file in plain English and it can be edited simply by loading it in the editor or word processor of your choice 10 See the text file KinFmt31 txt that is included in the Mage package that can be downloaded from any of the sites listed in the Editorial on p 107 of this issue 118 L C Freeman et al Social Networks 20 1998 109 118 The MAGE program does have one important limitation for use in social network research It makes it difficult to display directed relations two points are either connected or they are not and there is no simple way to display a directional tie Other than that however MAGE seems ideal for network applications References Arabie P Hubert L J De Soete G Eds 1996 Clustering and Classification World Scientific River Edge NJ Blau P M Duncan O D 1967 The American Occupational Structure Wiley New York Borgatti S P Everett M G Freeman L C 1992 UCINET IV network analysis software Connections 15 12 15 Brewer D 1995 Patterns in the recall of persons in the department of a formal organization J Quant Anthropol 5 255 284 Caldwell M A Peplau L A 1982 Sex differences in same sex friendship Sex Roles 8 721 732 Coombs G 1973 Networks and exchange the role of
18. raphic presentations for Best Friends and for Close Friends call attention to details in the overall patterning of the friendship structure in the residence details that might be less obvious without these images In the Best Friends for example two notable distinctions are evident A comparison of the ties within Wing A with those within Wing B immediately reveals that many more residents in Wing B have best friends who live on different floors whereas in Wing A only two pairs of best friends do not live on the same floor When examining the same sex friendship ties note that the male best friends are segregated into two tight clusters and one dyad whereas the female and opposite sex best friends are much more spread along both the x and y dimensions In the Close Friends image the impact of proximity between Wing A and Wing B is prominent All in all then this kind of visual display seems to capture a number of the essential details of the friendship structure of the residence hall L C Freeman et al Social Networks 20 1998 109 118 115 Now we turn to the second data set Here we will show the ability of MAGE to go beyond standard analysis and permit investigators to develop new insights about their structural data 4 The Kirke data set Kirke 1996 interviewed teenagers in suburban Dublin Ireland and asked them to name their best friends good friends boy or girl friends friends and pals Then she took the
19. se locations were the inputs to the MAGE program To start to explore the structure presented in this image try spinning the image along its horizontal axis Place the cursor on the left edge of the screen halfway between the 3 Romney and Weller 1984 first described this phenomenon You will have to download the self extracting DATA package along with the self extracting MAGE package from any of the sites listed in the Editorial on p 107 of this issue Then when you execute the MAGE package you will end up with an executable MAGE program and a text file When you execute the DATA package it will produce a couple of data files including one called webster kin You will need to run MAGE Then click on Proceed Pull down the File menu hit Openfile and open webster kin View the image by clicking your mouse button with the cursor over the black window L C Freeman et al Social Networks 20 1998 109 118 113 top and the bottom press the primary mouse key and move the mouse and therefore the cursor to the right It is immediately clear that this image has a more complicated structural form than the one we could see in the static projection of Fig 1 The residence data it seems contain more structural patterning than that displayed in the three arms shown in Fig 1 Now the question is whether we can discover some of the bases for this patterning Two established factors that typically influence social affiliati
20. uster of females in yellow is apparent to the extreme left and an all male in gold cluster is at the top The amount of time living in the residence has a much more dramatic impact Both View 1 and View 2 show the first year residents to be much more 114 L C Freeman et al Social Networks 20 1998 109 118 spread along the y dimension and first year residents are the only ones at the bottom The residents who have lived in the hall for a longer period are more spread along the x dimension with only a few located towards the top of the y dimension This MAGE image also allows the ties linking pairs of actors to be displayed Hit the Best button under TIES to show ties colored in pinktint linking those residents who mutually named one another as best friends The Close friends button adds ties in bluetint for those who mutually named one another at least at the close friend level And the union of all of the mutual friendship based ties is seen in yellow by hitting the Friends button To this point we have not looked at the ties linking residents in any detail We have provided two additional series of images that take advantage of the fact that the data are valued Image 2 displays the information for mutual Best Friends and Image 3 shows the Close Friends those individuals who named one another as at least a close friend but not as mutual best friends Pull down the KINEMAGE window and select
21. year old boy 015092 who serves as a cutpoint linking the two The girls on the other hand form far looser structures Both female female structures are in fact trees they contain no cycles at all And finally all the males can reach one another without using girls as links but the two subsets of females are connected only through male intermediaries This exchange between Freeman and Kirke certainly suggests the potential of MAGE as a tool for exploring network data The new image produced by Freeman spurred Kirke to think about her data in new ways And those thoughts led to still newer images that produced other new insights This interchange clearly demonstrates the power of visual tools and MAGE in particular to provide new insights in the process of social network analysis 5 Conclusions We have shown how MAGE can play several roles in social network research Its visual images use dynamic three dimensional displays and color to help those engaged in network research to become aware of details of network structure that are not otherwise apparent As a consequence it becomes easy for research workers to see their data in different ways and therefore to develop new insights about their data These images of networks can moreover be used to facilitate communication of the results of network research to others And perhaps most important MAGE presents those results in a form that encourages viewers to try out their own pers
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