A block-structured model for banking networks across multiple countries

Advances in exponential random graph ( p*) models applied to a large social network

Missing data in networks: exponential random graph ( p∗) models for networks with non-respondents

An introduction to exponential random graph ( p*) models for social networks

Exponential random graph ( [formula omitted]) models for affiliation networks

We discuss measuring and detecting influential observations and outliers in the context of exponential family random graph (ERG) models for social networks. We focus on the level of the nodes of the network and consider those nodes whose removal would result in changes to the model as extreme or "central" with respect to the structural features that "matter". We construe removal in terms of two case-deletion strategies: the tie-variables of an actor are assumed to be unobserved, or the node is removed resulting in the induced subgraph. We define the difference in inferred model resulting from case deletion from the perspective of information theory and difference in estimates, in both the natural and mean-value parameterisation, representing varying degrees of approximation. We arrive at several measures of influence and propose the use of two that do not require refitting of the model and lend themselves to routine application in the ERGM fitting procedure. MCMC p values are obtained for testing how extreme each node is with respect to the network structure. The influence measures are applied to two well-known data sets to illustrate the information they provide. From a network perspective, the proposed statistics offer an indication of which actors are most distinctive in the network structure, in terms of not abiding by the structural norms present across other actors.

How do individuals structure their political discussion networks, and what factors systematically shape such patterns? While much research has focused on the effect of personality traits and one's motivations, abilities, and opportunities, network-structural factors present different principles of tie formations. Evidence from an Exponential Family Random Graph Model and the meta-analysis of an Exponential Random Graph Model (ERGM) from 20 different groups' networks indicated that the pattern of political discussions was shaped by general discussion and network-endogenous structural processes. Results suggest that informal discussions of individuals serve as the important foundations of political behavior, and the processes of citizens' everyday political interactions emerge through complex interactions that cannot be regressed to mere individuals' predispositions or pure social selection processes.

We use the exponential random graph models to understand the network structure and its generative process for the Japanese bipartite network of banks and firms. One of the well known and simple model of exponential random graph is the Bernoulli model which shows the links in the bank-firm network are not independent from each other. Another popular exponential random graph model, the two star model, indicates that the bank-firms are in a state where macroscopic variables of the system can show large fluctuations. Moreover, the presence of high fluctuations reflect a fragile nature of the bank-firm network.

The exponential random graph (ERGM) model is a commonly used statistical framework for studying the determinants of tie formations from social network data. To test scientific theories under ERGMs, statistical inferential techniques are generally used based on traditional significance testing using p-values. This methodology has certain limitations, however, such as its inconsistent behavior when the null hypothesis is true, its inability to quantify evidence in favor of a null hypothesis, and its inability to test multiple hypotheses with competing equality and/or order constraints on the parameters of interest in a direct manner. To tackle these shortcomings, this paper presents Bayes factors and posterior probabilities for testing scientific expectations under a Bayesian framework. The methodology is implemented in the R package BFpack. The applicability of the methodology is illustrated using empirical collaboration networks and policy networks.

In recent social network studies, exponential random graph (ERG) models have been used comprehensively to model global social network structure as a function of their local features. In this study, we describe the ERG models and demonstrate its use in modelling the changing communication network structure at Enron Corporation during the period of its disintegration. We illustrate the modelling on communication networks, and provide a new way of classifying networks and their performance based on the occurrence of their local features. Among several micro-level structures of ERG models, we find significant variation in the appearance of A2P (Alternating k-two-paths) network structure in the communication network during crisis period and non-crisis period. We also notice that the attribute of hierarchical positions of actors (i.e., high rank versus low rank staff) have impact on the evolution process of networks during crisis. These findings could be used in analyzing communication networks of dynamic project groups and their adaptation process during crisis which could lead to an improved understanding how communications network evolve and adapt during crisis.

Collaboration has become crucial in solving scientific problems in biomedical and health sciences. There is a growing interest in applying social network analysis to professional associations aiming to leverage expertise and resources for optimal synergy. As a set of computational and statistical methods for analyzing social networks, exponential random graph models (ERGMs) examine complex collaborative networks due to their uniqueness of allowing for non-independent variables in network modeling. This study took a review approach to collect and analyze ERGM applications in health sciences by following the protocol of a systematic review. We included a total of 30 studies. The bibliometric characteristics revealed significant authors, institutions, countries, funding agencies, and citation impact associated with the publications. In addition, we observed five types of ERGMs for network modeling (standard ERGM and its extensions—Bayesian ERGM, temporal ERGM, separable temporal ERGM, and multilevel ERGM). Most studies (80%) used the standard ERGM, which possesses only endogenous and exogenous variables examining either micro- (individual-based) or macro-level (organization-based) collaborations without exploring how the links between individuals and organizations contribute to the overall network structure. Our findings help researchers (a) understand the extant research landscape of ERGM applications in health sciences, (b) learn to control and predict connection occurrence in a collaborative network, and (c) better design ERGM-applied studies to examine complex relations and social system structure, which is native to professional collaborations.

Coexistence of species requires equalizing mechanisms that minimize fitness differences, which are balanced by stabilizing mechanisms that enhance negative intraspecific interactions versus interspecific ones. Here, we develop a simple theoretical framework that allows measuring the relative strength of intraspecific versus interspecific competition in dominance hierarchies. We use it to evaluate mechanisms promoting coexistence between two congeneric charr that compete for foraging positions, which strongly influence density-dependent growth and survival. Agonistic interactions (n=761) among 71 Dolly Varden Salvelinus malma and whitespotted charr Salvelinus leucomaenis were measured by snorkelling in two pools in the sympatric zone of a Hokkaido stream during two summers. Interspecific dominance hierarchies, analysed using three methods, were closely correlated with fish length but the species treated each other equally. Ranks for the most dominant fish in each pool, determined directly by knockout experiments, were also virtually identical to ranks by length. Similarly, exponential random graph modelling of the social networks provided no evidence that either species was dominant over the other. Instead, larger fish were more likely to win contests, especially over fish of the next lower ranks. These results demonstrated that the two species were nearly ecological equivalents in accessing key resources in this sympatric zone. Nearly identical growth and stable densities over 4years further supported this inference, although Dolly Varden were a minority (29% of the assemblage), a sign of some fitness difference. Detailed foraging observations coupled with two concurrent studies revealed an effective stabilizing mechanism. Dolly Varden shifted to feeding directly from the benthos when drifting invertebrates declined, a behaviour enhanced by morphological character displacement, thereby partitioning food resources and enhancing intraspecific competition while avoiding agonistic encounters with whitespotted charr. The plurality of evidence indicates that fitness differences between these ecologically equivalent species are small in this local assemblage, and balanced by resource partitioning, a modest stabilizing mechanism that promotes coexistence. The theoretical framework presented here is a useful tool to evaluate the strength of interspecific versus intraspecific competition, which combined with information on trade-offs in ecological performance can contribute to a mechanistic understanding of species coexistence.

Exponential random graph models (ERGMs) are increasingly applied to observed network data and are central to understanding social structure and network processes. The chapters in this edited volume provide a self-contained, exhaustive account of the theoretical and methodological underpinnings of ERGMs, including models for univariate, multivariate, bipartite, longitudinal and social-influence type ERGMs. Each method is applied in individual case studies illustrating how social science theories may be examined empirically using ERGMs. The authors supply the reader with sufficient detail to specify ERGMs, fit them to data with any of the available software packages and interpret the results.

The exponential random graph model (ERGM) is a class of stochastic models for network data widely applied in statistical social network analysis. The ERGM can be used to model a wide range of social processes. However, it is generally difficult to estimate due to its intractable normalizing constant. Markov chain Monte Carlo maximum likelihood (MCMC-ML) ERGM estimation is available but tends to be numerically unstable due to model degeneracy of particular specifications. Bayesian ERGM estimation is robust to model degeneracy and is a practical alternative to the MCMC-ML approach. Bayesian model selection is based on the Bayes factor which is the ratio of marginal likelihoods of concurring models. The research aim of this thesis is to estimate the marginal likelihood of the ERGM class using path sampling which is also called thermodynamic integration. Power posterior sampling is a discretized version of thermodynamic integration using a fixed path of tempering steps to transition from the prior distribution to the posterior distribution of interest. In this thesis, power posterior sampling is used both to integrate over the parameter space of the ERGM posterior distribution of interest and to yield an estimate of the respective intractable ERGM normalizing constant. Existing approaches of estimating the ERGM marginal likelihood rely on a non-parametric density approximation or a Laplace approximation. The proposed power posterior exchange algorithm with explicit evaluation of the likelihood (PPEA-EEL) does not require such approximations and yields a valid estimate of the ERGM marginal likelihood. As the PPEA-EEL is a computationally expensive approach involving many MCMC samples, new graphical methods to evaluate power posterior samples are developed. In this thesis a brief introduction to random graphs and network dependencies is given. The ERGM class is discussed and various dependency assumptions are illustrated. MCMC-ML ERGM estimation is applied to policy networks in Ghana, Senegal and Uganda. Bayesian ERGM estimation and Bayesian model selection are discussed. An overview is given on methods of estimating the marginal likelihood originating from importance sampling, namely bridge sampling, path sampling and power posterior sampling. The PPEA-EEL is applied to social network data and the numerical stability of the approach is evaluated.

Research on the mechanism of knowledge diffusion in the MOOC learning forum using ERGMs

Recent developments in exponential random graph ( p*) models for social networks