Directed network Laplacians and random graph models

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph model. We focus on two existing spectral approaches that build and analyse Laplacian-style matrices via the minimization of frustration and trophic incoherence. These algorithms aim to reveal directed periodic and linear hierarchies, respectively. We show that reordering nodes using the two algorithms, or mapping them onto a specified lattice, is associated with new classes of directed random graph models. Using this random graph setting, we are able to compare the two algorithms on a given network and quantify which structure is more likely to be present. We illustrate the approach on synthetic and real networks, and discuss practical implementation issues.

Download Full-text

Inferential Network Analysis with Exponential Random Graph Models

Political Analysis ◽

10.1093/pan/mpq037 ◽

2011 ◽

Vol 19 (1) ◽

pp. 66-86 ◽

Cited By ~ 213

Author(s):

Skyler J. Cranmer ◽

Bruce A. Desmarais

Keyword(s):

Network Analysis ◽

Random Graph ◽

Graph Model ◽

Network Data ◽

Exponential Random Graph Models ◽

Graph Models ◽

Random Graph Model ◽

General Acceptance ◽

Random Graph Models ◽

Exponential Random Graph

Methods for descriptive network analysis have reached statistical maturity and general acceptance across the social sciences in recent years. However, methods for statistical inference with network data remain fledgling by comparison. We introduce and evaluate a general model for inference with network data, the Exponential Random Graph Model (ERGM) and several of its recent extensions. The ERGM simultaneously allows both inference on covariates and for arbitrarily complex network structures to be modeled. Our contributions are three-fold: beyond introducing the ERGM and discussing its limitations, we discuss extensions to the model that allow for the analysis of non-binary and longitudinally observed networks and show through applications that network-based inference can improve our understanding of political phenomena.

Download Full-text

Antecedents of Border Management Network in El Paso, Texas: An Exponential Random Graph Model

Journal of Homeland Security and Emergency Management ◽

10.1515/jhsem-2016-0011 ◽

2018 ◽

Vol 15 (3) ◽

Cited By ~ 1

Author(s):

Jungwon Yeo

Keyword(s):

Random Graph ◽

El Paso ◽

Graph Model ◽

Exponential Random Graph Models ◽

Graph Models ◽

Random Graph Model ◽

Random Graph Models ◽

Border Regions ◽

Exponential Random Graph ◽

Management Context

AbstractDespite the growing interest in interorganizational border management, relatively little is known about antecedents that drive such coordination efforts emerging in and around border regions. This case study uses exponential random graph models to test hypotheses about the antecedents of a border management coordination network in El Paso, Texas. The analysis demonstrates that actors tend to build tightly closed relationships through bonding and clustering, while also seeking cross-sectoral partnerships. In addition, actors tend to build ties with public organizations, and with organizations that represent regional interests/issues in the border management context. The research discusses the findings and offers some policy and administrative implications to enhance actor relationships within the border management network.

Download Full-text

Modeling Unobserved Heterogeneity in Social Networks with the Frailty Exponential Random Graph Model

Political Analysis ◽

10.1017/pan.2017.23 ◽

2018 ◽

Vol 26 (1) ◽

pp. 3-19 ◽

Cited By ~ 7

Author(s):

Janet M. Box-Steffensmeier ◽

Dino P. Christenson ◽

Jason W. Morgan

Keyword(s):

Random Graph ◽

Network Formation ◽

Unobserved Heterogeneity ◽

Graph Model ◽

Monte Carlo Analysis ◽

Exponential Random Graph Models ◽

Graph Models ◽

Random Graph Model ◽

Random Graph Models ◽

Exponential Random Graph

In the study of social processes, the presence of unobserved heterogeneity is a regular concern. It should be particularly worrisome for the statistical analysis of networks, given the complex dependencies that shape network formation combined with the restrictive assumptions of related models. In this paper, we demonstrate the importance of explicitly accounting for unobserved heterogeneity in exponential random graph models (ERGM) with a Monte Carlo analysis and two applications that have played an important role in the networks literature. Overall, these analyses show that failing to account for unobserved heterogeneity can have a significant impact on inferences about network formation. The proposed frailty extension to the ERGM (FERGM) generally outperforms the ERGM in these cases, and does so by relatively large margins. Moreover, our novel multilevel estimation strategy has the advantage of avoiding the problem of degeneration that plagues the standard MCMC-MLE approach.

Download Full-text

A note on perfect simulation for Exponential Random Graph Models

ESAIM Probability and Statistics ◽

10.1051/ps/2019024 ◽

2020 ◽

Vol 24 ◽

pp. 138-147 ◽

Cited By ~ 1

Author(s):

Andressa Cerqueira ◽

Aurélien Garivier ◽

Florencia Leonardi

Keyword(s):

Markov Chain ◽

Random Graph ◽

Mixing Time ◽

Graph Model ◽

Glauber Dynamics ◽

Perfect Simulation ◽

Exponential Random Graph Models ◽

Graph Models ◽

Random Graph Model ◽

Exponential Random Graph

In this paper, we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling from the past method of Propp and Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.

Download Full-text

Advances in Exponential Random Graph Models

The Oxford Handbook of Social Networks ◽

10.1093/oxfordhb/9780190251765.013.18 ◽

2020 ◽

pp. 233-253

Author(s):

Dean Lusher ◽

Peng Wang ◽

Julia Brennecke ◽

Julien Brailly ◽

Malick Faye ◽

...

Keyword(s):

Social Networks ◽

Social Influence ◽

Random Graph ◽

Statistical Models ◽

Directed Network ◽

Exponential Random Graph Models ◽

Graph Models ◽

Random Graph Models ◽

Exponential Random Graph ◽

Recent Developments

This chapter presents recent developments in exponential random graph models (ERGMs), statistical models for social network structure. ERGMs assume that social networks are composed of various network substructures (or network configurations) like reciprocity, brokerage, or transitive closure, which, combined together, explain how the network came into being. The chapter also discusses recent developments for related models—auto-logistic actor attributes models (ALAAMs)—that examine social influence effects. The chapter focuses on three new types of models that have developed in the past few years: directed network models for social influence, multilevel extensions of ERGMs, and multilevel extensions of ALAAMs. The chapter concludes with three empirical applications to demonstrate what new possibilities exist in the application of these new statistical models for social networks to social science questions.

Download Full-text

Using ERGM (Exponential Random Graph Model) in Exploring Network Effects: A Case Study of Policy Networks

The Korean Association of Governance Studies ◽

10.26847/mspa.2019.29.1.35 ◽

2019 ◽

Vol 29 (1) ◽

pp. 35-61

Author(s):

Hyun Hee Park

Keyword(s):

Random Graph ◽

Network Effects ◽

Graph Model ◽

Policy Networks ◽

Exponential Random Graph Model ◽

Random Graph Model ◽

Exponential Random Graph

Download Full-text

Random graphs

10.1093/oso/9780198805090.003.0011 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Random Graph ◽

Random Graphs ◽

Large Scale ◽

Random Network ◽

Graph Model ◽

Clustering Coefficient ◽

Giant Component ◽

Random Graph Model ◽

Definition Of ◽

Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

Download Full-text