the social network groups at the University of Groningen and the University of Melbourne, and for the helpful suggestions of an anonymous reviewer. This article reviews new specifications for exponential random graph models proposed by Snijders, Pattison, Robins & Handcock (2006) and demonstrates their improvement over homogeneous Markov random graph models in fitting empirical network data. Not only do the new specifications show improvements in goodness of fit for various data sets, they also help to avoid the problem of near-degeneracy that often afflicts the fitting of Markov random graph models in practice, particularly to network data exhibiting high levels of transitivity. The inclusion of a new higher order transitivity statistic allows estimation of parameters of exponential graph models for many (but not all) cases where it is impossible to estimate parameters of homogeneous Markov graph models. The new specifications were used to model a large number of classical smallscale network data sets and showed a dramatically better performance than Markov graph models. We also review three current programs for obtaining maximum likelihood estimates of model parameters and we compare these Monte Carlo maximum likelihood estimates with less accurate pseudo-likelihood estimates. Finally we discuss whether homogeneous Markov random graph models may be superseded by the new specifications, and how additional elaborations may further improve model performance. 2 In recent years, there has been growing interest in exponential random graph

A plausible representation of relational information among entities in dynamic systems such as a living cell or a social community is a stochastic network which is topologically rewiring and semantically evolving over time. While there is a rich literature on modeling static or temporally invariant networks, much less has been done toward modeling the dynamic processes underlying rewiring networks, and on recovering such networks when they are not observable. We present a class of hidden temporal exponential random graph models (htERGMs) to study the yet unexplored topic of modeling and recovering temporally rewiring networks from time series of node attributes such as activities of social actors or expression levels of genes. We show that one can reliably infer the latent timespecific topologies of the evolving networks from the observation. We report empirical results on both synthetic data and a Drosophila lifecycle gene expression data set, in comparison with a static counterpart of htERGM. 1.

Recent advances in statistical network analysis based on the family of exponential random graph (ERG) models have greatly improved our ability to conduct inference on dependence in large social networks

Curved exponential family models are a useful generalization of exponential random graph models (ERGMs). In particular, models involving the alternating k-star, alternating k-triangle, and alternating ktwopath statistics of Snijders et al. [Snijders, T.A.B., Pattison, P.E., Robins, G.L., Handcock, M.S., in press. New specifications for exponential random graph models. Sociological Methodology] may be viewed as curved exponential family models. This article unifies recent material in the literature regarding curved exponential family models for networks in general and models involving these alternating statistics in particular. It also discusses the intuition behind rewriting the three alternating statistics in terms of the degree distribution and the recently introduced shared partner distributions. This intuition suggests a redefinition of the alternating k-star statistic. Finally, this article demonstrates the use of the statnet package in R for fitting models of this sort, comparing new results on an oft-studied network dataset with results found in the literature.

We describe some of the capabilities of the ergm package and the statistical theory underlying it. This package contains tools for accomplishing three important, and interrelated, tasks involving exponential-family random graph models (ERGMs): estimation, simulation, and goodness of fit. More precisely, ergm has the capability of approximating a maximum likelihood estimator for an ERGM given a network data set; simulating new network data sets from a fitted ERGM using Markov chain Monte Carlo; and assessing how well a fitted ERGM does at capturing characteristics of a particular network data set.

The animation of network visualizations poses technical and theoretical challenges. Rather stable patterns are required before the mental map enables a user to make inferences over time. In order to enhance stability, we developed an extension of stressminimization with developments over time. This dynamic layouter is no longer based on linear interpolation between independent static visualizations, but change over time is used as a parameter in the optimization. Because of our focus on structural change versus stability the attention is shifted from the relational graph to the latent eigenvectors of matrices. The approach is illustrated with animations for the journal citation environments of Social Networks, the (co-)author networks in the carrying community of this journal, and the topical development using relations among its title words. Our results are also compared with animations based on PajekToSVGAnim and SoNIA.

Theoretical foundation of Response mechanisms in networks of online learners are revealed by Statistical Analysis of p * Markov Models for the Networks. Our comparative analysis of two networks shows that the minimal-effort hunt-for-social-capital mechanism controls a major behavior of both networks: negative tendency to respond. Differences in designs of the networks enhance certain mechanisms while suppressing others: cognition balance, predicted by the theories of cognitive balance, and peer pressure, predicted by the theories of collective action are enhanced in a team like network but suppressed in a Q&A like forum. On the other hand, exchange mechanism, predicted by the theory of exchange & resource dependency and tutor’s responsibility mechanism are enhanced in the Q&A type forum but suppressed in the team like network. Contagion mechanism, predicted by the theory of collective action did not develop in both networks. The different mechanisms lead to the formation of different micro and macro structures in the topologies of the responses of the networks and hence in the buildup of collaborative knowledge. The techniques presented in this work can be extended to other types of mechanisms and networks.

Existing template-independent web data extraction approaches adopt highly ineffective decoupled strategies—attempting to do data record detection and attribute labeling in two separate phases. In this paper, we propose an integrated web data extraction paradigm with hierarchical models. The proposed model is called Dynamic Hierarchical Markov Random Fields (DHMRFs). DHMRFs take structural uncertainty into consideration and define a joint distribution of both model structure and class labels. The joint distribution is an exponential family distribution. As a conditional model, DHMRFs relax the independence assumption as made in directed models. Since exact inference is intractable, a variational method is developed to learn the model’s parameters and to find the MAP model structure and label assignments. We apply DHMRFs to a real-world web data extraction task. Experimental results show that: (1) integrated web data extraction models can achieve significant improvements on both record detection and attribute labeling compared to decoupled models; (2) in diverse web data extraction DHMRFs can potentially address the blocky artifact issue which is suffered by fixed-structured hierarchical models.

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important real world applications such as spam detection, uncovering the hidden thematic structures in the Web and link recommendation. Counting triangles in graphs with millions and billions of edges requires algorithms which run fast, use small amount of space, provide accurate estimates of the number of triangles and preferably are parallelizable. In this paper we present an efficient triangle counting approximation algorithm which can be adapted to the semistreaming model [23]. The key idea of our algorithm is to combine the sampling algorithm of [51,52] and the partitioning of the set of vertices into a high degree and a low degree subset respectively as in [5], treating each set appropriately. From a mathematical perspective, we show a simplified proof of [52] which uses the powerful Kim-Vu concentration inequality [31] based on the Hajnal-Szemerédi theorem [25]. Furthermore, we improve bounds of existing triple sampling ( techniques based on a theorem of Ahlswede and Katona [3]. We obtain a running time O m + m3/2 log n tɛ2) and an (1 ± ɛ)

The statnet suite of R packages contains a wide range of functionality for the statistical analysis of social networks, including the implementation of exponential-family random graph (ERG) models. In this paper we illustrate some of the functionality of statnet through a tutorial analysis of a friendship network of 1,461 adolescents.