Applications of Social Network Analysis to Community Dynamics

Transcription

1 Applcatons of Socal Network Analyss to Communty Dynamcs A Thess Submtted for the Degree of Master of Scence (Engg.) n the Faculty of Engneerng by Koll Namsha Supercomputer Educaton and Research Centre Indan Insttute of Scence Bangalore Inda February 2008

2 Sr Venkateswaraya Namaha To My Parents & Brother

3 ACKNOWLEDGEMENT I am eternally grateful to my research supervsor, Prof. N. Balakrshnan for hs nvgoratng gudance and valuable suggestons durng the course of my research work. I thank hm for encouragng my deas and very patently correctng my mstakes. I am also ndebted to hm for hs utmost support, encouragement and nspraton throughout the perod of ths work. I am thankful to hm for always makng tme for me through hs hectc schedule. My specal thanks to my grandfather Prof. M. S. Murthy and my aunt Dr. Y. V. S. Lakshm for beng a great source of nspraton throughout my lfe. I also thank my grandmother Mrs. M. Sunanda and my uncle Mr. Y. K. Vswanath for always beng there for me. I dedcate all of my work to my beloved Parents, Mr. K. Staram Prasad, Dr. K. R. L. Suryakran and to my brother K. Sshr, who have always been the drvng force for all my achevements. My heartful apprecatons to all my frends, Mrs. Shjesta Vctor, Ms. Jeyanth, Ms. Shvagama Sundar, Ms. B. S. Soumya and Ms. P. Syamala and many other frends for extendng a helpng hand and makng my stay at IISc very memorable. I would lke to acknowledge the support of Mr. Ryan who helped me n all possble ways and have contnuously kept my sprts hgh. Specal thanks to Ms. Swarna, Ms. Nagaratna, Mr. Vshwas, Mr. Rav and Mr. Sas for ther tmely support throughout my tenure. I also thank SERC and the MMSL lab for provdng us the best computng facltes. It was a great joy to work n such a lab. I would also lke to extend my sncere thanks to all Professors at IISc, who shared ther knowledge wth us.

4 ABSTRACT Ths thess concerns Socal Network Analyss as a mechansm for explorng Communty Dynamcs. To be able to use the Socal Network methodologes, relatonshps exstng between the modelng enttes are requred. In ths thess, we use two dfferent knds of relatonshps: e-mals exchanged and co-authorshp of papers. The e-mals exchanged, as an ndcator of nformaton exchange n an organzaton, s used to facltate the emergence of structure wthn the organzaton. In ths thess we demonstrate the effectveness of usng e-mal communcaton patterns for crss detecton n a herarchcally set organzaton. We compare the performance of a Socal Network based Classfer wth some of the tradtonal classfers from the data mnng framework for nferrng ths herarchy. A generc framework for studyng dynamc group transformatons s presented and the co-authorshp of papers, as an ndcator of collaboraton n an academc nsttuton, s used to study the communty behavoral patterns evolvng over tme. Enron e-mal corpus and the IISc Co-authorshp Dataset are utlzed for llustratve purposes.

5 CONTENTS Acknowledgement Abstract Contents Lst of Fgures Lst of Tables v v v Chapter 1 Introducton Emergence of a New Scence Communtes of Practce Socal Networks Socal Network as Dscplne How s Socal Network Data Dfferent Propertes of Socal Networks Socal Network Methods Revew Work on Socal Networks Motvaton Organzaton of the Thess 19 Chapter 2 Organzatonal Herarchy from E-mal Communcatons Introducton Problem Descrpton Background Methodology Classfcaton Methods Enron E-mal Dataset Dfferent versons of Enron E-mal Corpus Enron Related Work Modfed Enron Dataset (Our Corpus) Enron Herarchy Data Experments and Results Dscusson of Results 49

6 2.8 Conclusons and Future Work 53 Chapter 3 Organzatonal Crss Detecton from E-mal Communcatons Introducton Background Enron-Events Methodology Feature Extracton Identfcaton of Informal Networks Results and Dscusson Conclusons and Future Work 78 Chapter 4 Evoluton of Communtes Introducton Problem Framework Background IISc Co-publcaton Data IISc Co-authorshp Dataset I IISc Co-authorshp Dataset II Methodology Clusterng Communty Transtons Extractng Communty Transtons Results Dscusson Conclusons and Future Work 110 Chapter 5 Summary Summary of Contrbutons Future Work 112 References 114

7 LIST OF FIGURES Fgure 1.1 Dstrbuton of Degree Vs Number of Nodes 2 Fgure 2.1 Vorono Cells n 2-D and 3-D 30 Fgure 2.2 K-Nearest Neghbor 30 Fgure 2.3 Example of Decson Tree 31 Fgure 2.4 Sgnal Flow Graph of a Sngle Perceptron 34 Fgure 2.5 Sgnal Flow Graph of a Mult-layer Perceptron 34 Fgure 2.6 Regular Equvalence Example 38 Fgure 2.7 Enron Database Schema 46 Fgure 2.8 Performance of Classfers 48 Fgure 2.9 Varatons n the Performance of the Socal Network Classfer wth 52 respect to E-mals Consdered Fgure 3.1 Varaton n the Traffc generated wth Events n Enron 70 Fgure 3.2 Varaton n Dstnct Senders wth the Events n Enron 70 Fgure 3.3 Varaton n Dstnct Recevers wth the Events n Enron 71 Fgure 3.4 Varaton n Reachablty wthn two hops wth Events n Enron 72 Fgure 3.5 Varaton n Reachablty wthn three hops wth Events n Enron 72 Fgure 3.6 Varaton n Group Closeness Centralty wth Events n Enron 73 Fgure 3.7 Varaton n the No. of Clques wth Events n Enron 74 Fgure 3.8 Varaton n the No. of n-clans wth Events n Enron 75 Fgure 3.9 Varaton n the number of Informal Networks wth Events n 76 Enron Fgure 3.10 Varaton n the Performance of Socal Network Classfer 77 Wth Events n Enron Fgure 4.1 Proposed Framework 82 Fgure 4.2 Dstrbuton n the No. of Authors wth ther Actve Years 87 Fgure 4.3 Dstrbuton of Authors year-wse wth No. of Actve years 87 Fgure 4.4 Dstrbuton n the No. of Papers wth varyng Actve years 88 Fgure 4.5 Dstrbuton of Authors year-wse wth No. of Actve Years 88 v

8 Fgure 4.6 Dstrbuton of Authors n IISc Co-authorshp Dataset I 90 Fgure 4.7 Dstrbuton of Papers n IISc Co-authorshp Dataset I 90 Fgure 4.8 Dstrbuton of Authors n IISc Co-authorshp Dataset II 91 Fgure 4.9 Dstrbuton of Papers n IISc Co-authorshp Dataset II 92 Fgure 4.10 Dstrbuton of Communtes n IISc Co-authorshp Dataset I 98 Fgure 4.11 Dstrbuton of Communtes n IISc Co-authorshp Dataset II 99 Fgure 4.12 Contnuaton n IISc Co-authorshp Dataset I 100 Fgure 4.13 Contnuaton n IISc Co-authorshp Dataset II 100 Fgure 4.14 Creaton n IISc Co-authorshp Dataset I 101 Fgure 4.15 Creaton n IISc Co-authorshp Dataset II 102 Fgure 4.16 Dssoluton n IISc Co-authorshp Dataset I 102 Fgure 4.17 Dssoluton n IISc Co-authorshp Dataset II 103 Fgure 4.18 Mergng n IISc Co-authorshp Dataset I 104 Fgure 4.19 Mergng n IISc Co-authorshp Dataset II 104 Fgure 4.20 Splttng n IISc Co-authorshp Dataset I 105 Fgure 4.21 Splttng n IISc Co-authorshp Dataset II 105 Fgure 4.22 Dstrbuton of each transformaton n IISc Co-authorshp 106 Dataset I Fgure 4.23 Dstrbuton of each transformaton n IISc Co-authorshp 107 Dataset II Fgure 4.24 Communty Sze Vs Domnant Member Actvty 109 In Co-authorshp Set I Fgure 4.25 Communty Sze Vs Domnant Member Actvty 110 In IISc Co-authorshp Dataset II v

9 LIST OF TABLES Table 2.1 Classfcaton Algorthms used 26 Table 2.2 Broad Ttles n Enron 47 Table 2.3 Overall Accuracy of Classfers 49 Table 2.4 Example Format for Correctly Vs Incorrectly classfed statstcs 50 for a ttle-classfer par Table 2.5 Correctly Vs Incorrectly classfed statstc for every ttle- 51 classfer par Table 3.1 Snapshot of Events assocated wth Enron crss 60 v

10 Chapter 1 INTRODUCTION 1.1. EMERGENCE OF A NEW SCIENCE Many systems take the form of networks, sets of nodes or vertces joned together n pars by lnks or edges. Examples nclude acquantance networks and collaboraton networks, technologcal networks such as the Internet, the Worldwde Web, and power grds, and bologcal networks such as neural networks, food webs, and metabolc networks. All these systems are networks, but all are completely dstnct n one sense or another. So, n essence what we requre s a language for talkng about networks that s precse enough to descrbe not only what a network s but also what knds of dfferent networks there are n the world [1]. Out of ths requrement, over decades of theory and experment n many felds from physcs to socology, s the emergence of a new scence, a scence of networks. In 1967, socal psychologst Stanley Mlgram performed an experment to solve an unresolved hypothess crculatng n those days. The hypothess was called the small-world problem. The clam of the small-world phenomenon s that the world, s n a sense small, when vewed as a network of socal acquantances, could be reached through a network of frends n a only a few steps. Mlgram asked a few hundred randomly selected people to send letters to a stock broker n Boston va ntermedares. They can send the letter to people they knew on frst name bass. Among the letters that reached the destnaton correctly, the average path length was found to be sx. Ths led to the phrase sx degrees of separaton. Ths experment lad the stage for algorthmc aspects ths new and emergng scence. In order to make such a clam, nstead of askng, How small s our world, one could ask, What would t take for any world to be small? In other words, we want to construct a mathematcal model of the world n whch the ndvduals are represented as nodes and relatonshps are represented as edges. Ths allows analyss usng tools of mathematcs. Erdos & Reny [2] ntroduced the theory of random graphs. A random graph s a network of nodes connected by lnks n a purely random fashon. Let N be the number of nodes. A par of nodes has probablty p of beng connected. 1

11 If k < 1: small, solated clusters small dameters short path lengths At k = 1: a gant component appears dameter peaks path lengths are hgh For k > 1: almost all nodes connected dameter shrnks path lengths shorten Percentage of nodes n largest component Dameter of largest component (not to scale) Phase transton k Fgure 1.1 Dstrbuton of Degree vs Number of Nodes Therefore, the average degree s k pn. What nterestng thngs can be sad for dfferent values of p or k? ( that are true as N ). What does ths mean? If connectons between people can be modeled as a random graph, then, because the average person easly knows more than one person (k >> 1), we lve n a small world where wthn a few lnks, we are connected to anyone n the world COMMUNITIES OF PRACTICE Why s the above fndng so surprsng? Imagne one has one hundred frends, each one of them also has hundred frends. So at one degree of separaton one connects to one hundred people and at two degrees connects to one hundred tmes one hundred. Proceedng n a smlar fashon, n fve degrees he s connected to nne bllon people. So f everyone has one hundred frends, then wthn sx steps he can connect hmself to the entre populaton. But there s one mportant omsson n ths reasonng. Chances are that one wll come up wth many of the same people n one s frends network. Ths observaton turns out to be a unversal feature n all networks. They dsplay what we call clusterng. We tend to have groups of frends, each of whch s lke a communty or 2

12 cluster based on shared experence, locaton, or nterests, joned to each other by overlaps created when ndvduals n one group also belong to other groups. Ths s partcularly relevant, because clusterng breeds redundancy and ts study can tell us a great deal about the networks. The ablty to detect communty structure n a network could have practcal applcatons. Communtes n a network mght represent real socal groupngs, perhaps by nterest or background; communtes n a ctaton network mght represent related papers on a sngle topc; communtes n a metabolc network mght represent cycles and other functonal groupngs; communtes on the web mght represent pages on related topcs; hdden communtes mght represent potental suspcous actvty. Beng able to dentfy these communtes could help us understand and explot these networks more effectvely. Communtes of practce are the collaboraton groups that naturally grow and coalesce wthn any knd of networks. Any nsttuton that provdes opportuntes for communcaton or nteracton among ts members s eventually threaded by communtes who have smlar goals and a shared understandng of ther actvtes. These communtes have been the subject of much research as a way to uncover the structure and nteracton patterns wthn a network n order to understand the collectve behavor of the network from the ndvduals that consttute the network. Recent Research on these networks has focused on usng a socal network perspectve to analyze these networks. A socal network conssts of both a set of actors, who may be arbtrary enttes lke persons or organzatons, and one or more types of relatons between them, such as nformaton exchange or economc relatonshp SOCIAL NETWORKS Socal Networks as a dscplne Networks have been studed as graphs n mathematcs, physcs, socology, engneerng and computer scence, bology and economcs. Each feld has ts own theory of networks and each feld has ts own way of aggregatng collectve behavor. So why s ths new? In the past, the networks have been vewed as objects of pure structure whose propertes are fxed n tme. Both these assumptons 3

13 are far from truth. Real networks represent populatons of ndvdual components that are actually dong somethng-nvolved n communcaton, generatng power, sendng data, or even makng decsons. Here, the structure of ndvdual components s mportant because they affect ther ndvdual behavor or the behavor of the system as a whole. Also, the networks are dynamc objects, not because thngs happened n these systems, but because the networks themselves are evolvng and changng n tme, wth respect to actvtes or decsons of the ndvdual components. Therefore, what happens and how t happens depend on the network, whch n turn depends on what has happened prevously. It s ths vew of the network- a contnuously evolvng and self consttutng system [1] - that s new about the scence of networks. If ths s to succeed, the new scence of networks must become a manfestaton of ts own subject matter, a network of scentsts collectvely solvng problems that cannot be solved by any sngle ndvdual or any sngle dscplne [1]. Socal network analyss (SNA) s a set of research procedures for dentfyng structures n systems based on the relatons among actors. Grounded n graph and system theores, ths approach has proven to be a powerful tool for studyng networks n physcal and socal worlds, ncludng on the web [3, 4, 5]. SNA focuses on relatons and tes n studyng actor s behavor and atttudes. Thus the postons of actors wthn a network and the strength of tes between them become crtcally mportant. Socal poston can be evaluated by fndng the centralty of a node dentfed through a number of connectons among network members. Such measures are used to characterze degrees of nfluence, promnence and mportance of certan members [6]. Te strength mostly nvolves closeness of bond. There s general agreement that strong tes contrbute to ntensve resource exchange and close communtes, whereas weak tes provde ntegraton of relatvely separated socal groups nto larger socal networks [7, 8]. The noton of a socal network and the methods of socal network analyss have attracted consderable nterest from the socal and behavoral and computer scence communty n recent decades. Much of ths nterest can be attrbuted to the appealng focus of socal network analyss on relatonshps among socal enttes, and on the patterns and mplcatons of these relatonshps. From the vew of socal network analyss, the presence of regular patterns n relatonshp, are referred as 4

14 structure and the quanttes that measure structure as structural varables. The focus on relatons, and the patterns of relatons, requres a set of methods and analytc concepts that are dstnct from the methods of tradtonal statstcs and data analyss How s Socal Network Data dfferent? On one hand, there really sn't anythng about socal network data that s all that unusual. Socal network analysts do use a specalzed language for descrbng the structure and contents of the sets of observatons that they use. But, network data can also be descrbed and understood usng the deas and concepts of more famlar methods, lke cross-sectonal survey research. On the other hand, the data sets that socal network analysts develop usually end up lookng qute dfferent from the conventonal rectangular data array so famlar to survey researchers and statstcal analysts. The dfferences are qute mportant because they lead us to look at our data n a dfferent way and even lead us to thnk dfferently about how to apply statstcs. "Conventonal" data consst of a rectangular array of measurements. The rows of the array are the cases, or subjects, or observatons. The columns consst of scores (quanttatve or qualtatve) on attrbutes, or varables, or measures. Ths data structure leads us to compare how actors are smlar or dssmlar to each other across attrbutes (by comparng rows). Or, we examne how varables are smlar or dssmlar to each other n ther dstrbutons across actors (by comparng or correlatng columns). "Socal Network" data consst of a square array of measurements. The rows of the array are the cases, or subjects, or observatons. The columns of the array are the same set of cases, subjects, or observatons. Each cell of the array descrbes a relatonshp between the actors. We could look at ths data structure the same way as wth attrbute data. By comparng rows of the array, we can see whch actors are smlar to whch other actors n whom they choose. By lookng at the columns, we can see who s smlar to whom n terms of beng chosen by others. These are useful ways to look at the data, because they help us to see whch actors have smlar postons n the network. Ths s the frst major emphass of network analyss: seeng how actors are located or embedded n the overall network. The analyst also notes 5

15 the densty of overall tes. The analyst mght also compare the cells above and below the dagonal to see f there s recprocty n choces. Ths s the second major emphass of network analyss: seeng how the whole pattern of ndvdual choces gves rse to more holstc patterns. It s qute possble to thnk of the network data set n the same terms as "conventonal data." One can thnk of the rows as smply a lstng of cases, and the columns as attrbutes of each actor (.e. the relatons wth other actors can be thought of as attrbutes of each actor). Indeed, many of the technques used by network analysts (lke calculatng correlatons and dstances) are appled exactly the same way to network data as they would be to conventonal data. Whle t s possble to descrbe network data as just a specal form of conventonal data, network analysts look at the data n some rather fundamentally dfferent ways. Rather than thnkng about how an actor's tes wth other actors descrbes the attrbutes of that actor, network analysts nstead see a structure of connectons, wthn whch the actor s embedded. Actors are descrbed by ther relatons, not by ther attrbutes. And, the relatons themselves are just as fundamental as the actors that they connect. The major dfference between conventonal and network data s that conventonal data focuses on actors and attrbutes; network data focus on actors and relatons. The dfference n emphass s consequental for the choces that a researcher must make n decdng on research desgn, n conductng samplng, developng measurement, and handlng the resultng data. It s not that the research tools used by network analysts are dfferent from those of other scentsts (they mostly are not). But the specal purposes and emphases of network research do call for some dfferent consderatons. From our survey, there are four major crtera that have been used n pror works to nfer relatonshps. They are self-report, communcaton, smlarty, and co-occurrence. Self-report s the most drect, and perhaps the most relable, crteron as t accepts only the lnks reported by the concerned actors themselves. For an actor reportng an assocate could mean revealng the assocate n questonnares or ntervews, acknowledgng the assocate n personal profle or home pages, or ncludng ths assocate n Instant Messagng buddy lst. As ths reportng s done ndvdually by 6

16 each actor, self reported lnks are not always mutual or equally weghted n both drectons. Communcaton s also a strong expresson of relatonshp, especally f the acts of communcaton are especally frequent or ntense (perhaps judges by what s exchanged or the length of conversaton). Partcularly, Internet-based communcaton tools, such as emals, newsgroups, and Instant Messagng, often leave electronc trals that can be traced and mned. Communcaton-based networks may consst of ether drected edges (from sender to recever) or undrected edges (f an exchange s requred). Smlarty borrows the dea from socology that people who are more closely related tend to have greater smlarty to each other. The problem of fndng undrected or mutual lnks between pars of actors can then be reduced to fndng smlar pars. Smlarty may be defned n terms of varous dstance functons and varous attrbutes, such as havng smlar content and lnkages n personal home pages, usng smlar vocabulary n emal messages, or sharng smlar opnons on common areas of nterest. Co-occurrence n turn s based on the dea that enttes that keep occurrng together at a frequency that s hgher than random chance usually allows are lkely to have some assocaton between them. Basc co-occurrence assumes that the dea would provde transactons, or clearly defned nstances of co-occurrence by a subset of actors. For nstance, a transacton could be a web page, and two names that keep occurrng together on the same web pages may be related. Alternatvely, a transacton could be a publcaton, and two authors who keep co-authorng papers together are also lkely to be related. Also the nodes or actors ncluded n non-network studes tend to be the result of ndependent probablty samplng. Network studes are much more lkely to nclude all of the actors who occur wthn some (usually naturally occurrng) boundary. The use of whole populatons as a way of selectng observatons n network studes makes t mportant for the analyst to be clear about the boundares of each populaton to be studed, and how ndvdual unts of observaton are to be selected wthn that populaton. Network data sets also frequently nvolve several levels of 7

17 analyss, wth actors embedded at the lowest level. Survey research methods usually use a qute dfferent approach to decdng whch nodes to study. A lst s made of all nodes (sometmes stratfed or clustered), and ndvdual elements are selected by probablty methods. The logc of the method treats each ndvdual as a separate replcaton that s, nterchangeable wth any other. The populatons that network analysts study are remarkably dverse. At one extreme, they mght consst of symbols n texts or sounds n verbalzatons, at the other extreme, natons n the world system of states mght consttute the populaton of nodes. Most common are populatons of ndvdual persons. In each case, however, the elements of the populaton to be studed are defned by fallng wthn some boundary. Network analysts can expand the boundares of ther studes by replcatng populatons. Rather than studyng one neghborhood, we can study several. Ths type of desgn (whch could use samplng methods to select populatons) allows for replcaton and for testng of hypotheses by comparng populatons. A second and equally mportant way that network studes expand ther scope s by the ncluson of multple levels of analyss, or modaltes. Most socal network analysts thnk of ndvdual persons as beng embedded n networks that are embedded n networks that are embedded n networks. Network analysts descrbe such structures as "mult-modal." A data set that contans nformaton about two types of socal enttes (say persons and organzatons) s a two mode network. Of course, ths knd of vew of the nature of socal structures s not unque to socal network analysts. Statstcal analysts deal wth the same ssues as "herarchcal" or "nested" desgns. Theorsts speak of the macro-meso-mcro levels of analyss, or develop schema for dentfyng levels of analyss (ndvdual, group, organzaton, communty, nsttuton, socety, global order beng the most commonly used system). One advantage of network thnkng and method s that t naturally predsposes the analyst to focus on multple levels of analyss smultaneously. That s, the network analyst s always nterested n how the ndvdual s embedded wthn a structure and how the structure emerges from the mcro-relatons between ndvdual parts. The ablty of network methods to map such mult-modal relatons s, at least potentally, a step forward n rgor. In one way, there s lttle apparent dfference between conventonal statstcal 8

18 approaches and network approaches. Unvarate, b-varate, and even many multvarate descrptve statstcal tools are commonly used n the descrbng, explorng, and modelng socal network data. Socal network data are easly represented as arrays of numbers, just lke other types of data. As a result, the same knds of operatons can be performed on network data as on other types of data. Algorthms from statstcs are commonly used to descrbe characterstcs of ndvdual observatons (e.g. the medan te strength of an actor wth all other actors n the network) and the network as a whole (e.g. the mean of all te strengths among all actors n the network). Statstcal algorthms are very heavly used n assessng the degree of smlarty among actors, and for fndng patterns n network data (e.g. factor analyss, cluster analyss, mult-dmensonal scalng). Even the tools of predctve modelng are commonly appled to network data (e.g. correlaton and regresson). The other major use of statstcs s for testng hypotheses. The key lnk n the nferental chan of hypothess testng s the estmaton of the standard errors of statstcs. But, n fact, t s not really dfferent from the logc of testng hypotheses wth non-network data. Socal network data tend to dffer from more "conventonal" survey data n some key ways: network data are often not probablty samples, and the observatons of ndvdual nodes are not ndependent. These dfferences are qute consequental for both the questons of generalzaton of fndngs, and for the mechancs of hypothess testng. There s, however, nothng fundamentally dfferent about the logc of the use of descrptve and nferental statstcs wth socal network data Propertes of Socal Networks Researchers have concentrated partcularly on a few propertes that seem to be common to many networks: the small-world property, power-law degree dstrbutons, and network transtvty. Small world effect s the fndng that the average dstance between vertces n a network s short, usually scalng logarthmcally wth the total number n of vertces. Rght-skewed degree dstrbuton s another property that many networks possess. The degree of a vertex n a network s the number of other vertces to whch t s connected, and one fnds that there are typcally many vertces n a network wth low degree and a small number wth hgh degree, the precse dstrbuton follow a power-law or exponental form. 9

19 A thrd property that many networks have n common s network transtvty, whch s the property that two vertces that are both neghbors of the same thrd vertex have a heghtened probablty of also beng neghbors of each other. In the language of socal networks, two of your frends wll have a greater probablty of knowng one another than wll two people chosen at random from the populaton, on account of ther common acquantance wth you Socal Network Methods Many of the key structural measures and notons of socal network analyss are motvated by central concepts n socal theory. Of crtcal mportance for the development of methods for socal network analyss s the fact that the unt of analyss n the network s not the ndvdual, but an entty consstng of a collecton of ndvduals and the lnkages among them. Network methods focus on dyads, trads or larger systems. Therefore, specal methods are necessary. It s mportant to contrast approaches n whch networks and structural propertes are central wth approaches that employ network deas and measurements n standard ndvduallevel analyses. The socal network perspectve models the relatonshps to depct the structure of a group. One could then study the mpact of ths structure on the functonng of the group and the nfluence of the structure on ndvduals wthn the group. It can also be used to study the process of change wthn a group over tme. Thus, the network perspectve also extends longtudnally. The socal network perspectve thus has a dstnctve orentaton n whch structures, ther mpact, and ther evoluton become prmary focus. Snce structures may be behavoral, socal, poltcal, or economc, socal network analyss thus allows a flexble set of concepts and methods wth broad nterdscplnary appeal. Before we look at related methods of socal networks, we frst revew the termnologes frequently used n these lteratures. An actor s a socal entty. It could be a person or any other entty for whch a relatonshp wth another entty could be defned. The relatonshp between a par of actors s called a te, lnk or par. Each lnk may be drected or undrected, bnary (present or absent) or weghted (a set of values, usually wth hgher value mplyng stronger relatonshp). Lnks could also be of partcular types, e.g., frendshp, famlal. All lnks of the same type can be 10

20 grouped together as a relaton. A dyad conssts of a par of actors and the tes between them. A trad s a subset of three actors and the tes among them. Relatonshps among larger subsets of actors nclude the subgroup or a group. Socal network encompasses a set of actors and all the relatons that could be defned on them. Usually dependng on the number of actor types n, a socal network may be dentfed as beng an n-mode network. As far as possble, these terms wll be unformly used throughout the rest of ths thess. There are many dfferent types of socal networks that can be studed. One way of categorzng them s based on mode. A mode s defned as the number of sets of enttes on whch the structural varables are measured. One-mode networks study just a sngle set of actors, whle two-mode networks focus on two sets of actors, or one set of actors and one set of events. There are many ways to descrbe socal network data mathematcally. The most popular of them are graph theoretc, socometrc and algebrac. For some forms of data and network methods, one notaton scheme may be preferred to the others. Graph theoretc notaton s most useful for centralty and prestge methods, cohesve subgroup deas, dyadc and tradc methods. Socometrc notaton refers to the representaton of data for each relaton n a two-way matrx, termed socomatrx. Socometrc notaton s often used for the study of structural equvalence and block models. Algebrac notaton s most approprate for role and postonal analyss and relatonal algebras. Both graph theory and matrx operatons have served as the foundatons of many concepts n the analyss of socal networks. One of the prmary uses of graph theory n socal network analyss s the dentfcaton of the most mportant actors n a socal network. All measures of mportance, attempt to descrbe and measure propertes of actor locaton n a socal network. Actors who are the most mportant are usually located n strategc locatons wthn the network. Several measures are defned based on degree, closeness, betweenness, nformaton and rank. These defntons yeld actor ndces whch attempt to quantfy the promnence of an ndvdual actor embedded n a network. The actor ndces can also be aggregated across actors to obtan a sngle group-level ndex whch summarzes how varable or dfferentated the set of actors s as a whole wth respect to a gven measure. Both centralty and prestge are examples of measures of the promnence or mportance of the actors n a socal network. 11