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38
The structure and function of complex networks
 SIAM REVIEW
, 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
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Cited by 1405 (9 self)
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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Assessing Degeneracy in Statistical Models of Social Networks
 Journal of the American Statistical Association
, 2003
"... discussions. This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (Wasserman and Pattison 1996) are a generalization of the Markov random graph models introduced by Frank ..."
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Cited by 55 (14 self)
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discussions. This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (Wasserman and Pattison 1996) are a generalization of the Markov random graph models introduced by Frank and Strauss (1986), which in turn are derived from developments in spatial statistics (Besag 1974). These models recognize the complex dependencies within relational data structures. A major barrier to the application of random graph models to social networks has been the lack of a sound statistical theory to evaluate model fit. This problem has at least three aspects: the specification of realistic models, the algorithmic difficulties of the inferential methods, and the assessment of the degree to which the graph structure produced by the models matches that of the data. We discuss these and related issues of the model degeneracy and inferential degeneracy for commonly used estimators.
NeighborhoodBased Models for Social Networks
 Sociological Methodology
, 2002
"... Harrison White and several anonymous reviewers for valuable comments on the work. We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of i ..."
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Cited by 54 (4 self)
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Harrison White and several anonymous reviewers for valuable comments on the work. We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of interaction and corresponds to a subset of possible network ties. In this paper, we discuss hypotheses about the form of these neighborhoods, and we present two new and theoretically plausible ways in which neighborhoodbased models for networks can be constructed. In the first, we introduce the notion of a setting structure, a directly hypothesized (or observed) set of exogenous constraints on possible neighborhood forms. In the second, we propose higherorder neighborhoods that are generated, in part, by the outcome of interactive network processes themselves. Applications of both approaches to model construction are presented, and the developments are considered within a general conceptual framework of locale for social networks. We show how assumptions about neighborhoods can be cast within a hierarchy of increasingly complex models; these models represent a progressively greater capacity for network processes to “reach ” across a network through long cycles or semipaths. We argue that this class of models holds new promise for the development of empirically plausible models for networks and networkbased processes. 2 1.
Discrete temporal models of social networks
, 2010
"... We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including maximum likelihood estimation algorithms. We discuss models of th ..."
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Cited by 31 (4 self)
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We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including maximum likelihood estimation algorithms. We discuss models of this type and their properties, and give examples, as well as a demonstration of their use for hypothesis testing and classification. We believe our temporal ERG models represent a useful new framework for modeling timeevolving social networks, and rewiring networks from other domains such as gene regulation circuitry, and communication networks.
A sequential importance sampling algorithm for generating random graphs with prescribed degrees
, 2006
"... Random graphs with a given degree sequence are a useful model capturing several features absent in the classical ErdősRényi model, such as dependent edges and nonbinomial degrees. In this paper, we use a characterization due to Erdős and Gallai to develop a sequential algorithm for generating a ra ..."
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Cited by 22 (0 self)
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Random graphs with a given degree sequence are a useful model capturing several features absent in the classical ErdősRényi model, such as dependent edges and nonbinomial degrees. In this paper, we use a characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows surprisingly efficient sequential importance sampling. Applications are given, including simulating a biological network and estimating the number of graphs with a given degree sequence. 1. Introduction. Random
Markov Chain Monte Carlo for Statistical Inference
 University of Washington, Center for
, 2000
"... These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent... ..."
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Cited by 18 (0 self)
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These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent...
p_2: A Random Effects Model with Covariates for Directed Graphs
, 2004
"... A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node. Par ..."
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Cited by 15 (2 self)
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A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node. Parameter estimates are proposed that are based on an iterated generalized least squares procedure. An application is presented to a data set on friendship relations between American lawyers.
Comparing networks across space and time, size and species
 Sociological Methodology
"... *We acknowledge the helpful comments of the editor and anonymous reviewers. For their encouragement and suggestions on the research, we thank H. Russell Bernard, Linton Freeman, and A. Kimball Romney. We thank Tracy Burkett and Douglas Nigh for making their data available to us.Comparing Networks Ac ..."
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Cited by 14 (1 self)
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*We acknowledge the helpful comments of the editor and anonymous reviewers. For their encouragement and suggestions on the research, we thank H. Russell Bernard, Linton Freeman, and A. Kimball Romney. We thank Tracy Burkett and Douglas Nigh for making their data available to us.Comparing Networks Across Space and Time, Size and Species We describe and illustrate methodology for comparing networks from diverse settings. Our empirical base consists of 42 networks from four kinds of species (humans, nonhuman primates, nonprimate mammals, and birds) and covering distinct types of relations such as influence, grooming, and agonistic encounters. The general problem is to determine whether networks are similarly structured despite their surface differences. The methodology we propose is generally applicable to the characterization and comparison of networklevel social structures across multiple settings, such as different organizations, communities, or social groups, and to the examination of sources of variability in network structure. We first fit a p * model (Wasserman and Pattison 1996) to each network to obtain estimates for effects of six structural properties on the probability of the graph. Then we calculate predicted tie probabilities for each network, using both its own parameter estimates and the estimates from each other network in the collection. Comparison is based on the similarity between sets of predicted tie probabilities. We then use correspondence analysis to represent the similarities among all 42 networks and interpret the resulting configuration using information about the species and relations involved. Results show that similarities among the networks are due more to the kind of relation than to the kind of animal. 2
Different Aspects of Social Network Analysis
 In Proceedings of the 2006 IEEE/WIC/ACM International Conference on the Web Intelligence (WI06), Hong Kong
, 2006
"... Abstract — A social network is a set of people (or organizations or other social entities) connected by a set of social relationships, such as friendship, coworking or information exchange. Social network analysis focuses on the analysis of patterns of relationships among people, organizations, sta ..."
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Cited by 14 (0 self)
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Abstract — A social network is a set of people (or organizations or other social entities) connected by a set of social relationships, such as friendship, coworking or information exchange. Social network analysis focuses on the analysis of patterns of relationships among people, organizations, states and such social entities. Social network analysis provides both a visual and a mathematical analysis of human relationships. Web can also be considered as a social network. Social networks are formed between Web pages by hyperlinking to other Web pages. In this paper a state of the art survey of the works done on social network analysis ranging from pure mathematical analyses in graphs to analyzing the social networks in Semantic Web is given. The main goal is to provide a road map for researchers working on different aspects of Social Network Analysis. I.