A survey on exponential random graph models: an application perspective

Ghafouri, Saeid; Khasteh, Seyed Hossein

doi:10.7717/peerj-cs.269

Cited by 22 publications

(5 citation statements)

References 91 publications

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“…The ERGM, known as the P* (P-star) model, assumes a wide conditional dependency among the connections in the network. Specifically, suppose the other connections in the network have been determined; in that case, there is a conditional dependency between two specific links, and the conditional probability of the simultaneous existence of the two links is unequal to the product of the marginal conditional probabilities of the two links [73]. The statistical items that are considered in the P* model are not only for network features but also for attribute features of network members.…”

Section: Exponential Random Graph Models (Ergm)mentioning

confidence: 99%

Evolution and Impacting Factors of Global Renewable Energy Products Trade Network: An Empirical Investigation Based on ERGM Model

Liu

Yang

et al. 2023

Sustainability

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Global trade of renewable energy products has increased significantly in recent years. This paper constructs an analytical framework of a global trade network for renewable energy products based on bilateral trade data between 2009 and 2019. It analyses its structural evolution at the global and local levels and investigates the influencing factors of the network with the Exponential Random Graph Model. The empirical results indicate that countries in the trade network have become more closely connected, featuring a core-periphery and increasing reciprocity relationship. China, Germany, and Japan have remained in the position of core countries; China has especially been prominent among core countries. Our empirical results verify that the sender-receiver effects can explain the evolution of this global trade network. The empirical results also indicate that the climate change agreement network and the common border network have positive effects on the formation of the trade network. As regards political implications, the core countries in the trade network should optimize the layout of renewable energy development and improve infrastructure accordingly. Countries should also jointly build a more fair and reasonable multilateral system that fulfills their responsibilities.

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Section: Exponential Random Graph Models (Ergm)mentioning

confidence: 99%

Evolution and Impacting Factors of Global Renewable Energy Products Trade Network: An Empirical Investigation Based on ERGM Model

Liu

Yang

et al. 2023

Sustainability

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“…Network data are collected and analyzed in various scientific fields, including the social sciences (e.g., social or friendship networks, marriage, sexual partnerships); academic paper networks (collaboration or citation networks); neuroscience (human brain networks and interactions); political science (international relations, wars between countries, insurgencies, terrorist networks, strategic alliances and friendships); education (multilevel student relation data, item response data); economics (financial markets, economic trading or resource distribution networks); epidemiology (disease spread dynamics, HIV, COVID-19); physics (Ising models, finding parsimonious mechanisms of network formation); biology and other natural sciences (protein-protein, molecular interaction, metabolic, cellular, genetic, ecological, and food web networks); artificial intelligence and machine learning (finding missing link in a business or a terrorist network, recommender systems, Netflix, neural networks); spatial statistics (discrete Markov random fields); traffic systems and transportation networks (roads, railways, airplanes); cooperation in an organization (advice giving in an office, identity disambiguation, business organization analysis); communication patterns and networks (detecting latent terrorist cells); telecommunications (mobile phone networks); and computer science and networks (e-mail, internet, blogs, web, Facebook, Twitter(X), LinkedIn, information spread, viral marketing, gossiping, dating networks, blockchain network, virus propagation). Network science has seen many reviews due to its longtime scientific and societal impacts (Wasserman & Faust, 1994;Newman 2003;Goldenberg et al 2010;Snijders, 2011;Pastor-Satorras & Vespignani, 2004;Raval & Ray, 2013;Newman 2018;Horvat & Zweig, 2018;Brodka & Kazienko 2018;Ghafouri & Khasteh, 2020;Loyal & Chen 2020;Hammoud & Kramer 2020;Kinsley et al 2020;Caimo & Gollini, 2022). Meanwhile, the high dimensionality of network data poses challenges to modern statistical computing methods for network data analysis modeling.…”

Section: Overview Of Network Data Modelingmentioning

confidence: 99%

Approximate Bayesian computation using asymptotically normal point estimates

Karabatsos¹

2022

Comput Stat

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This paper introduces a novel Approximate Bayesian Computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihood functions. This framework can describe the possibly skewed and high dimensional posterior distribution by a novel multivariate copula-based distribution, based on univariate marginal posterior distributions which can account for skewness and be accurately estimated by Distribution Random Forests (DRF) while performing automatic summary statistics (covariates) selection, and on robustly estimated copula dependence parameters. The framework employs a novel multivariate mode estimator to perform for MLE and posterior mode estimation, and provides an optional step to perform model selection from a given set of models with posterior probabilities estimated by DRF. The posterior distribution estimation accuracy of the ABC framework is illustrated through simulation studies involving models with analytically computable posterior distributions, and involving exponential random graph and mechanistic network models which are each defined by an intractable likelihood from which it is costly to simulate large network datasets. Also, the framework is illustrated through analyses of large reallife networks of sizes ranging between 28,000 to 65.6 million nodes (between 3 million to 1.8 billion edges), including a large multilayer network with weighted directed edges.

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“…The p-star model, also called exponential random graph model, is one of the best-known and most widely used statistical models for social networks [13,17,18,26,35,40,41,43,44]. The model has been applied with success in applications related to fields such as communication, computer science, economics, physics, psychology, and sociology [1,16,38,42]. Compared with previous social network models, the main reason for its success is that the p-star model is able to represent interdependencies in a network.…”

Section: Preliminariesmentioning

confidence: 99%

Parameter estimation in a 3‐parameterp‐star random graph model

2020

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An important issue in social network analysis refers to the development of algorithms for estimating parameters of a social network model, using data available from the network itself. This entails solving an optimization problem. In the paper, we propose a new method for parameter estimation in a specific social network model, namely, the so‐called p‐star random graph model with three parameters. The method is based on the mean‐field approximation of the moments associated with the three subgraphs defining the model, namely: the mean numbers of edges, 2‐stars, and triangles. A modified gradient ascent method is applied to maximize the log‐likelihood function of the p‐star model, in which the components of the gradient are computed using approximate values of the moments. Compared to other existing iterative methods for parameter estimation, which are computationally very expensive when the number of vertices becomes large, such as gradient ascent applied to maximum log‐likelihood and maximum log‐pseudo‐likelihood estimation, the proposed approach has the advantage of a much cheaper cost per iteration, which is practically independent of the number of vertices.

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A survey on exponential random graph models: an application perspective

Cited by 22 publications

References 91 publications

Evolution and Impacting Factors of Global Renewable Energy Products Trade Network: An Empirical Investigation Based on ERGM Model

Evolution and Impacting Factors of Global Renewable Energy Products Trade Network: An Empirical Investigation Based on ERGM Model

Approximate Bayesian computation using asymptotically normal point estimates

Parameter estimation in a 3‐parameterp‐star random graph model

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