Statistical Models for Networks: A Brief Review of Some Recent Research

We begin with a graph (or a directed graph), a single set of nodes \(\mathcal{N}\), and a set of lines or arcs \(\mathcal{L}\). It is common to use this mathematical concept to represent a network. We use the notation of [1], especially Chapters 13 and 15. There are extensions of these ideas to a wide range of networks, including multiple relations, affiliation relations, valued relations, and social influence and selection situations (in which information on attributes of the nodes is available), all of which can be found in the chapters of [2].

[1]  D. Hunter,et al.  Inference in Curved Exponential Family Models for Networks , 2006 .

[2]  P. Pattison.  LOGIT MODELS AND LOGISTIC REGRESSIONS FOR SOCIAL NETWORKS: I. AN INTRODUCTION TO MARKOV GRAPHS AND p* STANLEY WASSERMAN UNIVERSITY OF ILLINOIS , 1996 .

[3]  M. Newman,et al.  Solution of the two-star model of a network. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  P. Holland,et al.  An Exponential Family of Probability Distributions for Directed Graphs , 1981 .

[5]  P. Pattison,et al.  Small and Other Worlds: Global Network Structures from Local Processes1 , 2005, American Journal of Sociology.

[6]  P. Pattison,et al.  New Specifications for Exponential Random Graph Models , 2006 .

[7]  Garry Robins,et al.  Network models for social selection processes , 2001, Soc. Networks.

[8]  Hung T. Nguyen,et al.  An Introduction to Random Sets , 2006 .

[9]  Alessandro Vespignani,et al.  Network Science: Theory, Tools, and Practice , 2012 .

[10]  David R. Hunter,et al.  Curved exponential family models for social networks , 2007, Soc. Networks.

[11]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: III. Valued relations , 1999 .

[12]  Luciano Rossoni,et al.  Models and methods in social network analysis , 2006 .

[13]  S. Wasserman,et al.  Models and Methods in Social Network Analysis: An Introduction to Random Graphs, Dependence Graphs, and p * , 2005 .

[14]  Peter D. Hoff,et al.  Latent Space Approaches to Social Network Analysis , 2002 .

[15]  Carolyn J. Anderson,et al.  A p* primer: logit models for social networks , 1999, Soc. Networks.

[16]  P. Pattison,et al.  Network models for social influence processes , 2001 .

[17]  D. J. Strauss,et al.  Pseudolikelihood Estimation for Social Networks , 1990 .

[18]  Peng Wang,et al.  Recent developments in exponential random graph (p*) models for social networks , 2007, Soc. Networks.

[19]  T. Snijders,et al.  Modeling the Coevolution of Networks and Behavior , 2007 .

[20]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[21]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp , 1996 .

[22]  Tom A. B. Snijders,et al.  Markov Chain Monte Carlo Estimation of Exponential Random Graph Models , 2002, J. Soc. Struct..

[23]  Garry Robins,et al.  An introduction to exponential random graph (p*) models for social networks , 2007, Soc. Networks.

[24]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: II. Multivariate relations. , 1999, The British journal of mathematical and statistical psychology.