Sep 082011

Intra-Organizational Network Conference (ION 5)

Call for Papers


Hosted by:

LINKS Center for Social Network Analysis

University of Kentucky

April 13-15, 2012



The mission of the LINKS Center is to promote a social network perspective on the study and management of organizations.  The ION conference brings together top scholars to present the latest research on social networks and management.  On April 13-15, 2012, in Lexington, KY, the LINKS center will host the ION Conference for the 5th time.

Confirmed speakers for ION 5 include:

Stephen P. Borgatti – Chellgren Chair of Management, University of Kentucky
Daniel J. Brass – J. Henning Hilliard Professor of Innovation Management, University of Kentucky
Ronald Burt – Hobart W. Williams Professor of Sociology and Strategy, University of Chicago

Martin Kilduff – Diageo Professor of Management Studies, Cambridge University
David Krackhardt – Professor of Organizations, Carnegie Mellon University


Open Submissions

The ION conference has been kept, in previous years, purposefully small to enable intense engagement and discussion. This year, we would like to invite up to five exceptional papers that focus on phenomena of relevance to the study of social networks in an organizational context.  Authors of accepted papers will have the opportunity to present their work to noted scholars in the field and receive quality feedback.  

Please submit a full paper for consideration to Giuseppe (Joe) Labianca by November 1, 2011.  The authors of approximately 5 selected papers will be notified by November 15, 2011.  There is no attendance or meal fee, but participants are expected to cover their own transportation and lodging expenses. 

ION 5 conference organizers:

Giuseppe (Joe) Labianca

Ajay Mehra

Theresa Floyd

Brandon Ofem



For more information, please refer to ION Conference website at:


LINKS Center website:

Sep 052011

There has been some time that I’m thinking about an option in Google + who let users to Suggest one or some of THEIR Social Circles to their other Friends. For example I have a social circle that includes people who are working about Social Network Analysis (SNA) and I want to introduce this circle to SNA interested researchers but I can’t. In search for this I found this website whose manager has been made some Social Circles in order to suggest others to follow them, he has make some Subject Categories and collected so famous people’s list under this categories. I have shared some of this suggestions link under the text in Related Links section.

But in Twitter you can make a public or private List of your contacts and you can Suggest this list to other interested people to follow the listed people’s Tweets. Here I have collected a Public List of people who are working about Social Network Analysis (SNA), So you can go there with your Twitter account and follow the whole people in the list with just one click and then after you can go under your following lists section to see these people’s Tweets. Now this list just contains 69 people but I’m working on it and trying to add more experts and SNA interested people to this list.

I suggest you to make some of these private or public lists in order not to mix people’s Tweets, for example OnlineSNA is now following 788 people on Twitter and has 120 followers (till now) and in my home stream there has so many Tweets from so many different people with various interests and I cannot read all of them at once, so I go to each lists particular page to see special people from that category with their specific Tweets around a subject matter.


You can read a PERSIAN version of this post HERE.

Related Links:






Sep 022011

In second post of SNA Related Links Collection I want to introduce these sites:

You can read a Persian introduction of this links HERE.


  • Financial network analysis (This is Kimmo Soramaki’s blog where he collects research on financial networks. The goal of financial network analysis is to enhance financial stability and unedrstand systemic risks better through analysing the flows of funds and the exposures between the diverse participants in the financial system.) I have checked this blog and unfortunately it is temporarily down, you can access a cached copy of that HERE.






You can read a Persian introduction of this links HERE.

Aug 302011

As First post of SNA Related Links collection of site I want to share five of most famous active websites working about Social Network Analysis (SNA).

You can read a Persian introduction of this links HERE.

  • ASA Section on Mathematical Sociology  (The ASA Section on Mathematical Sociology supports research on the representation, measurement, and modeling of social networks. The organization also co-sponsors a number of meetings and events)


You can read a Persian introduction of this links HERE.

Aug 262011

ASONAM 2012 Home page.


Here I have copied some information from ASONAM 2012 Homepage to inform SNA interested researchers about this conference that is one of leading events in this field:

You can read a Persian description of this conference in HERE.




The 2012 International Conference on Advances in Social Networks Analysis and Mining

The study of of social networks originated in social and business communities. In recent years, social network research has advanced significantly; the development of sophisticated techniques for Social Network Analysis and Mining (SNAM) has been highly influenced by the online social Web sites, email logs, phone logs and instant messaging systems, which are widely analyzed using graph theory and machine learning techniques. People perceive the Web increasingly as a social medium that fosters interaction among people, sharing of experiences and knowledge, group activities, community formation and evolution. This has led to a rising prominence of SNAM in academia, politics, homeland security and business. This follows the pattern of known entities of our society that have evolved into networks in which actors are increasingly dependent on their structural embedding.

The international conference on Advances in Social Network Analysis and Mining (ASONAM 2012) will primarily provide an interdisciplinary venue that will bring together practitioners and researchers from a variety of SNAM fields to promote collaborations and exchange of ideas and practices. ASONAM 2012 is intended to address important aspects with a specific focus on the emerging trends and industry needs associated with social networking analysis and mining. The conference solicits experimental and theoretical works on social network analysis and mining along with their application to real life situations.


Keynote Speakers

Barry Wellman, University of Toronto
Title : TBA


Scientific Topics

  • Anomaly detection in social network evolution
  • Application of social network analysis
  • Application of social network mining
  • Communities discovery and analysis in large scale online social networks
  • Communities discovery and analysis in large scale offline social networks
  • Connection between biological similarities and social network formulation
  • Contextual social network analysis
  • Crime data mining and network analysis
  • Cyber anthropology
  • Dark Web
  • Data protection inside communities
  • Detection of communities by document analysis
  • Economical impact of social network discovery
  • More…

You can read a Persian description of this conference in HERE.

Related Links:

-Barry Wellman HomePage (Keynote Speaker)
Aug 262011


This post includes a very simple text I found on The Study of Social that deals with comparing Facebook, Twitter and Google + structures in Social Network Analysis words.

Social Network Structures of Twitter, Facebook and Google + and their Impacts on Information Flow


by: Nitin Mayande (@nima87700 on Twitter)

Tuesday, August 23, 2011 at 7:00AM

There has been a ton of hype lately over Google+ and how it is going to kill Twitter or Facebook or both. People are all wound up comparing feature sets from one platform to another but there are some critical fundamentals we have to understand first about how information flows. I wanted to take a minute to explore each of these and I would love your thoughts.

Let s look at the network structure of all the three networks. All the three networks have a very different network structure. People on Twitter tend to connect with people they find have similar interest because of which Twitter has a network structure that is mainly tends towards being small world . Once you identify your network of interest the information can be percolated to the right people quickly. Whereas Facebook is a network where people connect to people they already know and share their likes and dislikes with them. It s very rare that one would connect with somebody they don t already know therefore the network structure acquires more of scale free structure. In both these networks preferential attachment (why people choose to connect with somebody) occurs but the reasons for preferential attachment are quite different leading to different network structures.

The network structure has a huge impact on the how the information flows as a result changing what phenomenon s like influence mean. On Twitter people are influenced by the subject matter expert because the network structure supports the flow of expertise of an individual. A tweet on an interesting topic by a subject matter expert can reach people who are three to four degrees away from the expert and are not directly connected. This I believe is the reason why twitter is an effective place to run campaigns based on a subject.




Whereas people on Facebook are influenced by the likes and dislikes of the people they know and trust which is supported by the scale free network structure (I discussed these types of networks in my previous posts). The status update by an individual is interesting only to people in their first degree of network or at the most to a few in the second degree. That s why there is a need for a property like fanpage, where the intention is that if you trust a brand then people who trust you will also trust the brand. Therefore, Facebook really works well to keep people connected with the brand.

Coming back to Google+, It lets you segregate your network based on the concept of circles. What this means is that it effectively gives you an opportunity to connect with people who are interesting because of a subject (who you already know) and same time you can connect with people who are your personal friends. You can do all this on the same network while keeping these two groups separate all the time. The concept of circles lets you creates cliques (A) within you network and each clique can have a separate network structure (B). This has a huge impact on the underlying information flow and the reach of the network. It is very difficult for information to flow in this kind of a network structure. Formation of clique limits the exposure of information only to people in the circle thereby keeping the flow focused for an audience but at the same time limits the reach of information beyond the circle. But this provides Google with an opportunity to understand your interests (and do better ad targeting and improve search but does not necessarily mean you can find people with common interests, whom you don t already know.


There is another drawback too. Google + lets one manipulate with network structure by creating circles, unlike Twitter or Facebook where the network structure is organically created because of your interactions. What happens if you have few circles with too many people or too many circles with few people in each circle? In the first case you gain reach but lose focused audience in the second case you gain focused audience but loose reach. Attaining that right balance is difficult. As these networks are dynamic networks the right mix may be a moving target which creates more hassle than it s worth if not managed properly.


Aug 262011

The Study of Social – Social Network Structure


This post contains one of simple texts I found in The Study of Social about Social Network Structure. I hope it will be useful in introducing Social Network Analysis (SNA).

Social Network Structure


I have been talking a lot about network structure in my previous blogs. In this blog I shall provide a few preliminaries about network structure and how they are measured. A virtual community network structure is viewed in terms of nodes and ties. Nodes are individual actors within the network, and ties represent the flow of relationships between the actors. The relationships defined by linkages among units/nodes are a fundamental component of a virtual community (Wasserman & Faust, 1994). Social Network Analysis (SNA) techniques are used to visualize the patterns of interactions among participants on the virtual community. Metrics are often used to determine the roles of nodes in a network. Of these the most prominent are degree, closeness and betweenness. Degree is the sum of the links attached to a node. Closeness is the reciprocal of the sum of all the geodesic (shortest) distances from a given node to all others. A higher betweenness value for a node means that it is on higher number of shortest-paths between nodes, which is an indication of the node’s importance (Wasserman & Faust, 1994).

Virtual communities are characterized by both scale free and small world characteristics of a network (Klemm & Eguıluz, 2002). The scale free and small network characteristics are as follows:

Trees, Scale Free & Small World Networks

(a)     Tree Network




Networks that grow by attaching new nodes to existing nodes (by adding one edge only) form into trees. They have no cycles (Fig. a). If in this process the new nodes attach preferentially to existing nodes with a large number of edges, then the result is a scale-free network (Albert & Barabási, 2000). Scale-free networks are distinguished by three characteristics. First, they are highly clustered; if two vertices share a common neighbor, it is likely the two are themselves adjacent. Second, the average shortest path between two vertices is logarithmically small. And finally, the node degrees are distributed according to a power law.


(b)     Scale Free Network





In Scale Free networks the distribution of different network parameters act in an exponential fashion (Fig. b). The most interesting and most measured exponentially distributed parameter is the distribution of connections from each node outwards (Out Degree). This uneven distribution means that in these networks some of the members are connected to a lesser degree and some of the members are connected to a greater degree, which is how they hold a senior position in the network (Goh, et al., 2002). Networks of this type are relatively resilient, but are not at all immune to attack. In other words, a random removal of network members (a crash) will not hurt its stability, but a directed removal of keypoints will cause the network to quickly collapse. On Scale Free networks, the distribution of density or congestion is constant and is not dependent on the exponential coefficient of the distribution of the number of connections (Jeong, 2003).


(c)     Small World Network





A Small World network is a network in which most nodes are not neighbors of each other but most nodes can be reached by other nodes in the networks by hopping over a few nodes. These networks (Watts & Strogatz, 2003) form when long distance connections are added at random to regular networks (Fig. c). They are characterized by low paths lengths between nodes and high clustering coefficient. The Clustering Coefficient is the extent to which the nodes in the graph tend to create a unified group with many internal connections but few connections leading out of the group. The Clustering Coefficient can be seen as a measurement of the nodes’ isolation. The Characteristic Path Length (CPL) is a measurement of the average distance needed to pass from node to node. A network can be considered a Small World network when its CPL is similar to the CPL of a random network of the same length, but its CC is much larger (at least by a single order of magnitude) when compared to a similar random network. In other words, in Small World networks we will expect to find a large unified group; in networks such as these “hiding” is impossible (Herman, 2003).

I hope this clears up a few things and gives you an idea of what I mean by structure and how to measure the structure of a social network. Please feel free to ask me any clarifications and also share some of your methods that you use


Aug 192011

In this post, that has been written under My SNA projects section of site,  I wanted to share my M.A thesis’s abstract in order to share this projects’ results with interested researchers whose works are about Social Network Analysis of Online Social Networking Sites.

In future posts in My SNA Projects section, I will share some of results in form of SocioGraphs that has been generated by SNA softwares like Pajek.

Here you can read a Persian description of thesis and its abstract in Persian.


A Study on Online Social Networks; Case Study of Doreh and U24



Social Media and Web 2.0 applications that include several various kinds of Internet Services like social networking websites, micro-blogs, wikis, content sharing websites has been become more prevailing these days and its vast growth tend some researchers to see future of Media in web 2.0 and social networking Sites.(Creese, 2007) This thesis intends to show that Social Network Analysis (SNA) can be a useful method to study social networking Sites, to do so, and as two cases for testing this hypothesis that SNA is a useful method for studying Social Networking Sites, we have studied and , two online social networks whose aim are connecting Iranian universities’ students and experts to each other,  first with utilizing SNA, main structure of relationships in networks was extracted and then with Sociological approach we analyzed the collected data more in-depth. So, our method in this thesis was Social Network Analysis (SNA). After extracting infrastructure of relationships in these social networks, these relationships’ components including nodes (vertices) and edges (arcs) were analyzed by concepts of Graph theory with utilizing SNA software such as Ucinet, NodeXL and Pajek. After finding these social networks’ special features and attributes, we tried to answer some main questions like: Who are these networks’ most connected node? How do these people connect to each other in network? Do they make a special structure within the whole network? Our research results showed that these online social networks have a Core-Periphery structure, after that, to know more about these cores and their structures; we have designed a two step method for Doreh and a one step method for U24, and we tried to find their components, in first step our study showed that Doreh’s core consists of 16 connected Cohesive Subgroups that has 918 members, in second step, we found that these 16 groups also consisted of 6 more dense and connected Cohesive Subgroups that has 377 members;  and U24’s core consists of 7 connected Cohesive Subgroups that has 374 members. So we can conclude that with utilizing SNA, we have studied these networks’ structures and their cores’ components and with this we have reached some results that are not possible to achieve by other research methods. And as a general conclusion we can claim that Social Network Analysis (SNA) is a useful method in studying Social Networking Sites (SNS).

Keywords: Social Network Analysis (SNA), Social Networking Sites (SNS), Web 2.0, Social Media,,

Here you can read a Persian description of thesis and its abstract in Persian.

In future posts in My SNA Projects section, I will share some of results in form of SocioGraphs that has been generated by SNA softwares like Pajek.

Aug 162011

International Network for Social Network Analysis (INSNA)

This is first post in SNA sites part of website, here I want to introduce one of famous populated and leading associations in Social Network Analysis. As it is described in INSNA website:

INSNA is the professional association for researchers interested in social network analysis. The association is a non-profit organization incorporated in the state of Delaware and founded by Barry Wellman in 1978. ”

    • The principal functions of INSNA are as follows:
      • We publish Connections, a bulletin containing news, scholarly articles, technical columns, and abstracts and book reviews.
      • We sponsor the annual International Social Networks Conference (also known as Sunbelt).
      • We maintain electronic services:
        • This web site with features including discussion forums, I-Connect, bibliographies, publications, and much more.
        • SOCNET, a ListServ electronic discussion forum, and a link to REDES, a Spanish language network Listserv.
      • We maintain a database of information on members, selling a mailing list to selected publishers and educators.
      • We provide a way to subscribe to the journal of Social Networks, published by Elsevier.

Here you can read a Persian introduction of INSNA.

Aug 152011

Social Network Analysis; Methods and Applications

Stanley Wasserman and Katherine Faust


ISBN-10: 0521387078 | ISBN-13: 978-0521387071 |

Publication Date: November 25, 1994 | Edition: 1

In this post I wanted to introduce one of leading handbooks in Social Networks field titled as Social Network Analysis; Methods and Applications; in this books’ page in Amazon it has been introduced by these words:

Book Description:

Social network analysis, which focuses on relationships among social entities, is used widely in the social and behavioral sciences, as well as in economics, marketing, and industrial engineering. Social Network Analysis: Methods and Applications reviews and discusses methods for the analysis of social networks with a focus on applications of these methods to many substantive examples. As the first book to provide a comprehensive coverage of the methodology and applications of the field, this study is both a reference book and a textbook.”


Here I have written this book’s contents list, in near future I will write here what I have reached by reading this book and I will describe this book’s parts and chapters separately.

You can find a Persian description of this book here.


Part I: Networks, Relations, and Structure

1 Social Network Analysis in the Social and Behavioral Sciences 3
1.1 The Social Networks Perspective 4
1.2 Historical and Theoretical Foundations 10
1.2.1 Empirical Motivations 11
1.2,2 Theoretical Motivations 13
1.2.3 Mathematical Motivations 15
1.2.4 In Summary 16
1.3 Fundamental Concepts in Network Analysis 17
1.4 Distinctive Features 21
1.5 Organization of the Book and How to Read It 22
1.5.1 Complexity 23
1.5.2 DeSCriptive and Statistical Methods 23
1.5.3 Theory Driven Methods 24
1.5.4 Chronology 24
1.5.5 Levels of Analysis 25
1.5.6 Chapter Prerequisites 26
1.6 Summary 27
2 Social Network Data 28
2.1 Introduction: What Are Network Data? 28
2.1.1 Structural and Composition Variables 29
2.1.2 Modes 29
2.1.3 Affiliation Variables 30
2.2 Boundary Specification and Sampling 30
2.2.1 What Is Your Population? 31
2.2.2 Sampling 33
2.3 Types of Networks 35
2.3.1 One-Mode Networks 36
2.3.2 Two-Mode Networks 39
2.3.3 Ego-centered and Special Dyadic Networks 41
2.4 Network Data, Measurement and Collection 43
2.4.1 Measurement 43
2.4.2 Collection 45
2.4.3 Longitudinal Data Collection 55
2.4.4 Measurement Validity, Reliability, Accuracy, Error 56
2.5 Data Sets Found in These Pages 59
2.5.1 Krackhardt’s High-tech Managers 60
2.5.2 Padgett’s Florentine Families 61
2.5.3 Freeman’s EIES Network 62
2.5.4 Countries Trade Data 64
2.5.5 Galaskiewicz’s CEOs and Clubs Network 65
2.5.6 Other Data 66

Part II: Mathematical Representations of Social Networks 67

3 Notation for Social Network Data 69
3.1 Graph Theoretic Notation 71
3.1.1 A Single Relation 71
3.1.2 OMultiple Relations 73
3.1.3 Summary 75
3.2 Sociometric Notation 77
3.2.1 Single Relation 79
3.2.2 Multiple Relations 81
3.2.3 Summary 83
3.3 OAlgebraic Notation 84
3.4 OTwo Sets of Actors 85
3.4.1 (8)Different Types of Pairs 86
3.4.2 OSociometric Notation 87
3.5 Putting It All Together 89
4 Graphs and Matrices 92
4.1 Why Graphs? 93
4.2 Graphs 94
4.2.1 Subgraphs, Dyads, and Triads 97
4.2.2 Nodal Degree 100
4.2.3 Density of Graphs and Subgraphs 101
4.2.4 Example: Padgett’s Florentine Families 103
4.2.5 Walks, Trails, and Paths 105
4.2.6 Connected Graphs and Components 109
4.2.7 Geodesics, Distance, and Diameter 110
4.2.8 Connectivity of Graphs 112
4.2.9 Isomorphic Graphs and Subgraphs 117
4.2.10 OSpecial Kinds of Graphs 119
4.3 Directed Graphs 121
4.3.1 Subgraphs – Dyads 124
4.3.2 Nodal Indegree and Outdegree 125
4.3.3 Density of a Directed Graph 129
4.3.4 An Example 129
4.3.5 Directed Walks, Paths, Semipaths 129
4.3.6 Reachability and Connectivity in Digraphs 132
4.3.7 Geodesics, Distance and Diameter 134
4.3.8 OSpecial Kinds of Directed Graphs 134
4.3.9 Summary 136
4.4 Signed Graphs and Signed Directed Graphs 136
4.4.1 Signed Graph 137
4.4.2 Signed Directed Graphs 138
4.5 Valued Graphs and Valued Directed Graphs 140
4.5.1 Nodes and Dyads 142
4.5.2 Density in a Valued Graph 143
4.5.3 OPaths in Valued Graphs 143
4.6 Multigraphs 145
4.7 (8)Hypergraphs 146
4.8 Relations 148
4.8.1 Definition 148
4.8.2 Properties of Relations 149
4.9 Matrices 150
4.9.1 Matrices for Graphs 150
4.9.2 Matrices for Digraphs 152
4.9.3 Matrices for Valued Graphs 153
4.9.4 Matrices for Two-Mode Networks 154
4.9.5 OMatrices for Hypergraphs 154
4.9.6 Basic Matrix Operations 154
4.9.7 Computing Simple Network Properties 159
4.9.8 Summary 164
4.10 Properties 164
4.10.1 Reflexivity 164
4.10.2 Symmetry 165
4.10.3 Transitivity 165
4.11 Summary 165

Part III: Structural and Locational Properties 167

5 Centrality and Prestige 169
5.1 Prominence: Centrality and Prestige 172
5.1.1 Actor Centrality 173
5.1.2 Actor Prestige 174
5.1.3 Group Centralization and Group Prestige 175
5.2 Nondirectional Relations 177
5.2.1 Degree Centrality 178
5.2.2 Closeness Centrality
5.2.3 Betweenness Centrality
5.2.4 (8)Information Centrality
5.3 Directional Relations
5.3.1 Centrality
5.3.2 Prestige
5.3.3 A Different Example
5.4 Comparisons and Extensions
6 Strnctural Balance and Transitivity
6.1 Structural Balance
6.1.1 Signed Nondirectional Relations
6.1.2 Signed Directional Relations
6.1.3 OChecking for Balance
6.1.4 An Index for Balance
6.1.5 Summary
6.2 Clusterability
6.2.1 The Clustering Theorems
6.2.2 Summary
6.3 Generalizations of Clusterability
6.3.1 Empirical Evidence 239
6.3.2 ORanked Clusterability 240
6.3.3 Summary 242
6.4 Transitivity 243
6.5 Conclusion 247
7 Cohesive Subgroups 249
7.1 Background 250
7.1.1 Social Group and Subgroup 250
7.1.2 Notation 252
7.2 Subgroups Based on Complete Mutuality 253
7.2.1 Definition of a Clique 254
7.2.2 An Example 254
7.2.3 Considerations 256
7.3 Reachability and Diameter 257
7.3.1 n-cliques 258
7.3.2 An Example 259
7.3.3 Considerations 260
7.3.4 n-clans and n-clubs 260
7.3.5 Summary 262
7.4 Subgroups Based on Nodal Degree 263
7.4.1 k-plexes 265
7.4.2 k-cores 266
7.5 Comparing Within to Outside Subgroup Ties 267
7.5.1 LS Sets 268
7.5.2 Lambda Sets 269
7.6 Measures of Subgroup Cohesion 270
7.7 Directional Relations 273
7.7.1 Cliques Based on Reciprocated Ties 273
7.7.2 Connectivity in Directional Relations 274
7.7.3 n-cliques in Directional Relations 275
7.8 Valued Relations 277
7.8.1 Cliques, n-cliques, and k-plexes 278
7.8.2 Other Approaches for Valued Relations 282
7.9 Interpretation of Cohesive Subgroups 283
7.10 Other Approaches 284
7.10.1 Matrix Permutation Approaches 284
7.10.2 Multidimensional Scaling 287
7.10.3 OFactor Analysis 290
7.11 Summary 290
8 Affiliations and Overlapping Snbgroups 291
8.1 Affiliation Networks 291
8.2 Background 292
8.2.1 Theory 292
8.2.2 Concepts 294
8.2.3 Applications and Rationale 295
8.3 Representing Affiliation Networks 298
8.3.1 The Affiliation Network Matrix 298
8.3.2 Bipartite Graph 299
8.3.3 Hypergraph 303
8.3.4 OSimplices and Simplicial Complexes 306
8.3.5 Summary 306
8.3.6 An example: Galaskiewicz’s CEOs and Clubs 307
8.4 One-mode Networks 307
8.4.1 Definition 307
8.4.2 Examples 309
8.5 Properties of Affiliation Networks 312
8.5.1 Properties of Actors and Events 312
8.5.2 Properties of One-mode Networks 314
8.5.3 Taking Account of Subgroup Size 322
8.5.4 Interpretation 324
8.6 (8)Analysis of Actors and Events 326
8.6.1 (8)Galois Lattices 326
8.6.2 (8)Correspondence Analysis 334
8.7 Summary 342

Part IV: Roles and Positions 345

9 Strnctural Eqnivalence 347
9.1 Background 348
9.1.1 Social Roles and Positions 348
9.1.2 An Overview of Positional and Role Analysis 351
9.1.3 A Brief History 354
9.2 Definition of Structural Equivalence 356
9.2.1 Definition 356
9.2.2 An Example 357
9.2.3 Some Issues in Defining Structural Equivalence 359
9.3 Positional Analysis 361
9.3.1 Simplification of Multirelational Networks 361
9.3.2 Tasks in a Positional Analysis 363
9.4 Measuring Structural Equivalence 366
9.4.1 Euclidean Distance as a Measure of Structural
Equivalence 367
9.4.2 Correlation as a Measure of Structural Equivalence 368
9.4.3 Some Considerations in Measuring Structural
Equivalence 370
9.5 Representation of Network Positions 375
9.5.1 Partitioning Actors 375
9.5.2 Spatial Representations of Actor Equivalences 385
9.5.3 Ties Between and Within Positions 388
9.6 Summary 391
10 Blockmodels
10.1 Definition
10.2 Building Blocks
10.2.1 Perfect Fit (Fat Fit)
10.2.2 Zeroblock (Lean Fit) Criterion
10.2.3 Oneblock Criterion
10.2.4 ct Density Criterion
10.2.5 Comparison of Criteria
10.2.6 Examples
10.2.7 Valued Relations
10.3 Interpretation
10.3.1 Actor Attributes
10.3.2 Describing Individual Positions
10.3.3 Image Matrices
10.4 Summary
11 Relational Algebras 425
11.1 Background 426
11.2 Notation and Algebraic Operations 428
11.2.1 Composition and Compound Relations 429
11.2.2 Properties of Composition and Compound
Relations 432
11.3 Multiplication Tables for Relations 433
11.3.1 Multiplication Tables and Relational Structures 435
11.3.2 An Example 439
11.4 Simplification of Role Tables 442
11.4.1 Simplification by Comparing Images 443
11.4.2 (8)Homomorphic Reduction 445
11.5 (8)Comparing Role Structures 449
11.5.1 Joint Homomorphic Reduction 451
11.5.2 The Common Structure Semigroup 452
11.5.3 An Example 453
11.5.4 Measuring the Similarity of Role Structures 457
11.6 Summary 460
12 Network Positions and Roles 461
12.1 Background 462
12.1.1 Theoretical Definitions of Roles and Positions 462
12.1.2 Levels of Role Analysis in Social Networks 464
12.1.3 Equivalences in Networks 466
12.2 Structural Equivalence, Revisited 468
12.3 Automorphic and Isomorphic Equivalence 469
12.3.1 Definition 470
12.3.2 Example 471
12.3.3 Measuring Automorphic Equivalence 472
12.4 Regular Equivalence 473
12.4.1 Definition of Regular Equivalence 474
12.4.2 Regular Equivalence for Nondirectional Relations 475
12.4.3 Regular Equivalence Blockmodels 476
12.4.4 OA Measure of Regular Equivalence 479
12.4.5 An Example 481
12.5 “Types” of Ties 483
12.5.1 An Example 485
12.6 Local Role Equivalence 487
12.6.1 Measuring Local Role Dissimilarity 488
12.6.2 Examples 491
12.7 (8)Ego Algebras 494
12.7.1 Definition of Ego Algebras 496
12.7.2 Equivalence of Ego Algebras 497
12.7.3 Measuring Ego Algebra Similarity 497
12.7.4 Examples 499
12.8 Discussion 502

Part V: Dyadic and Triadic Methods

13 Dyads
13.1 An Overview
13.2 An Example and Some Definitions
13.3 Dyads
13.3.1 The Dyad Census
13.3.2 The Example and Its Dyad Census
13.3.3 An Index for Mutuality
13.3.4 (8)A Second Index for Mutuality
13.3.5 OSubgraph Analysis, in General
13.4 Simple Distributions
13.4.1 The Uniform Distribution – A Review
13.4.2 Simple Distributions on Digraphs
13.5 Statistical Analysis of the Number of Arcs
13.5.1 Testing
13.5.2 Estimation
13.6 (8)Conditional Uniform Distributions 535
13.6.1 Uniform Distribution, Conditional on the Number
of Arcs 536
13.6.2 Uniform Distribution, Conditional on the
13.7 Statistical Analysis of the Number of Mutuals
13.7.1 Estimation
13.7.2 Testing 542
13.7.3 Examples 543
13.8 (8)Other Conditional Uniform Distributions 544
13.8.1 Uniform Distribution, Conditional on the Indegrees 545
13.8.2 The UlMAN Distribution 547
13.8.3 More Complex Distributions 550
13.9 Other Research 552
13.10 Conclusion 555
14 Triads 556
14.1 Random Models and Substantive Hypotheses 558
14.2 Triads 559
14.2.1 The Triad Census 564
14.2.2 The Example and Its Triad Census 574
14.3 Distribution of a Triad Census 575
14.3.1 (8)Mean and Variance of a k-subgraph Census 576
14.3.2 Mean and Variance of a Triad Census 579
14.3.3 Return to the Example 581
14.3.4 Mean and Variance of Linear Combinations of a
Triad Census 582
14.3.5 A Brief Review 584
14.4 Testing Structural Hypotheses 585
14.4.1 Configurations 585
14.4.2 From Configurations to Weighting Vectors 590
14.4.3 From Weighting Vectors to Test Statistics 592
14.4.4 An Example 595
14.4.5 Another Example – Testing for Transitivity 596
14.5 Generalizations and Conclusions 598
14.6 Summary 601

Part VI: Statistical Dyadic Interaction Models 603

15 Statistical Analysis of Single Relational Networks 605
15.1 Single Directional Relations 607
15.1.1 The Y-array 608
15.1.2 Modeling the Y-array 612
15.1.3 Parameters 619
15.1.4 (8)Is PI a Random Directed Graph Distribution? 633
15.1.5 Summary 634
15.2 Attribute Variables 635
15.2.1 Introduction 636
15.2.2 The W-array 637
15.2.3 The Basic Model with Attribute Variables 640
15.2.4 Examples: Using Attribute Variables
15.3 Related Models for Further Aggregated Data
15.3.1 Strict Relational Analysis – The V-array
15.3.2 Ordinal Relational Data
15.4 ONondirectional Relations 656
15.4.1 A Model 656
15.4.2 An Example 657
15.5 (8)Recent Generalizations of PI 658
15.6 (8)Single Relations and Two Sets of Actors 662
15.6.1 Introduction 662
15.6.2 The Basic Model 663
15.6.3 Aggregating Dyads for Two-mode Networks 664
15.7 Computing for Log-linear Models
15.7.1 Computing Packages
15.7.2 From Printouts to Parameters
15.8 Summary
16 Stochastic Blockmodels and Goodness-of-Fit Indices
16.1 Evaluating Blockmodels
16.1.1 Goodness-of-Fit Statistics for Blockmodels
16.1.2 Structurally Based Blockmodels and Permutation
Tests 688
16.1.3 An Example 689
16.2 Stochastic Blockmodels 692
16.2.1 Definition of a Stochastic Blockmodel 694
16.2.2 Definition of Stochastic Equivalence 696
16.2.3 Application to Special Probability Functions 697
16.2.4 Goodness-of-Fit Indices for Stochastic Blockmodels 703
16.2.5 OStochastic a posteriori Blockmodels
16.2.6 Measures of Stochastic Equivalence
16.2.7 Stochastic Blockmodel Representations
16.2.8 The Example Continued
16.3 Summary: Generalizations and Extensions 719
16.3.1 Statistical Analysis of Multiple Relational Networks 719
16.3.2 Statistical Analysis of Longitudinal Relations 721

Part VII: Epilogue 725

17 Future Directions 727
17.1 Statistical Models 727
17.2 Generalizing to New Kinds of Data 729
17.2.1 Multiple Relations 730
17.2.2 Dynamic and Longitudinal Network Models 730
17.2.3 Ego-centered Networks 731
17.3 Data Collection 731
17.4 Sampling 732
17.5 General Propositions about Structure 732
17.6 Computer Technology 733
17.7 Networks and Standard Social and Behavioral Science 733

Appendix A Compoter Programs 735
Appendix B Data 738
References 756
Name Index 802
Subject Index 811
List of Notation 819

ISBN-10: 0521387078 | ISBN-13: 978-0521387071 | Publication Date: November 25, 1994 | Edition: 1