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Exponential Random Graph Models

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Encyclopedia of Social Network Analysis and Mining

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Synonyms

Exponential family of random graphs; Logit models; Markov graphs; Maximum entropy random networks; p* models; p-star models; p1 models

Glossary

Adjacency Matrix:

is a matrix with rows and columns labelled by graph vertices i and j, with elements A ij = 1 or 0 according to whether the vertices, i and j, are connected/adjacent or not. In the case of an undirected graph with no self-loops or multiple edges (the so-called simple graph), the adjacency matrix is symmetric (i.e., A ij = A ji ) and has 0 s on the diagonal (i.e., A ii = 0). Accordingly, for a simple directed graph, the symmetry condition may not be fulfilled, i.e., it can be that A ij ≠ A ji

Clustering:

describes tendency of nodes to cluster together. Clustering is measured by the clustering coefficient which calculates the average probability that two neighbors of a vertex are themselves nearest neighbors

Ensemble of Graphs:

means the set of all possible graphs (network realizations) that the (real-world) network may...

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Acknowledgments

A.F. acknowledges financial support from the Ministry of Science and Higher Education in Poland (national 3-year scholarship for outstanding young scientists, 2010–2013) and from the Foundation for Polish Science (grant no. POMOST/2012-5/5).

Author information

Authors and Affiliations

  1. Faculty of Physics, Warsaw University of Technology, Warsaw, Poland

    Agata Fronczak

Authors
  1. Agata Fronczak
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Corresponding author

Correspondence to Agata Fronczak .

Editor information

Editors and Affiliations

  1. Computer Science, University of Calgary, Calgary, Alberta, Canada

    Reda Alhajj

  2. University of Calgary Computer Science, Calgary, Canada

    Jon Rokne

Section Editor information

  1. Department of Computer Science and Management, Institute of Informatics, Wrocław University of Technology, Wrocław, Poland

    Przemysław Kazienko

  2. Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland

    Jaroslaw Jankowski

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Fronczak, A. (2016). Exponential Random Graph Models. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7163-9_233-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7163-9_233-1

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  • Print ISBN: 978-1-4614-7163-9

  • Online ISBN: 978-1-4614-7163-9

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