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ergm.graphlets: A Package for ERG Modeling Based on Graphlet Statistics

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  • Yaveroğlu, Ömer Nebil
  • Fitzhugh, Sean M.
  • Kurant, Maciej
  • Markopoulou, Athina
  • Butts, Carter T.
  • Pržulj, Nataša

Abstract

Exponential-family random graph models are probabilistic network models that are parametrized by sufficient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing environment is a collection of tools for the analysis of network data within an exponential-family random graph model framework. Many different network properties can be employed as sufficient statistics for exponential- family random graph models by using the model terms defined in the ergm package; this functionality can be expanded by the creation of packages that code for additional network statistics. Here, our focus is on the addition of statistics based on graphlets. Graphlets are classes of small, connected, induced subgraphs that can be used to describe the topological structure of a network. We introduce an R package called ergm.graphlets that enables the use of graphlet properties of a network within the ergm package of R. The ergm.graphlets package provides a complete list of model terms that allows to incorporate statistics of any 2-, 3-, 4- and 5-node graphlets into exponential-family random graph models. The new model terms of the ergm.graphlets package enable both exponential-family random graph modeling of global structural properties and investigation of relationships between node attributes (i.e., covariates) and local topologies around nodes.

Suggested Citation

  • Yaveroğlu, Ömer Nebil & Fitzhugh, Sean M. & Kurant, Maciej & Markopoulou, Athina & Butts, Carter T. & Pržulj, Nataša, 2015. "ergm.graphlets: A Package for ERG Modeling Based on Graphlet Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 65(i12).
    • Handle: RePEc:jss:jstsof:v:065:i12
    DOI: http://hdl.handle.net/10.18637/jss.v065.i12
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    1. Hunter, David R. & Handcock, Mark S. & Butts, Carter T. & Goodreau, Steven M. & Morris, Martina, 2008. "ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 24(i03).
    2. Morris, Martina & Handcock, Mark S. & Hunter, David R., 2008. "Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 24(i04).
    3. Stanley Wasserman & Philippa Pattison, 1996. "Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 401-425, September.
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    1. Lienert, Jeffrey & Koehly, Laura & Reed-Tsochas, Felix & Marcum, Christopher Steven, 2017. "An efficient counting method for the colored triad census," SocArXiv rd6kw, Center for Open Science.

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