Empirical reference distributions for networks of different size

Anna Smith, Catherine A. Calder, Christopher R. Browning

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features, across multiple networks that differ in size. Although "normalized" versions of some network statistics exist, we demonstrate via simulation why direct comparison is often inappropriate. We consider normalizing network statistics relative to a simple fully parameterized reference distribution and demonstrate via simulation how this is an improvement over direct comparison, but still sometimes problematic. We propose a new adjustment method based on a reference distribution constructed as a mixture model of random graphs which reflect the dependence structure exhibited in the observed networks. We show that using simple Bernoulli models as mixture components in this reference distribution can provide adjusted network statistics that are relatively comparable across different network sizes but still describe interesting features of networks, and that this can be accomplished at relatively low computational expense. Finally, we apply this methodology to a collection of ecological networks derived from the Los Angeles Family and Neighborhood Survey activity location data.

Original languageEnglish
Pages (from-to)24-37
Number of pages14
JournalSocial Networks
StatePublished - Oct 1 2016

Bibliographical note

Funding Information:
Support for this work was provided by grants from the National Science Foundation (NSF DMS-1209161 ), the National Institute of Health (NIH R01DA032371 ), the William T. Grant Foundation , and The Ohio State University Institute for Population Research (NIH P2CHD058484 ).

Publisher Copyright:
© 2016 Elsevier B.V.


  • ERGM
  • L.A.FANS
  • Mixture model
  • Network comparison
  • Normalized network statistics

ASJC Scopus subject areas

  • Anthropology
  • Sociology and Political Science
  • Social Sciences (all)
  • Psychology (all)


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