Exact sampling of graphs with prescribed degree correlations

Kevin E. Bassler, Charo I Del Genio, Péter L. Erds, I. Miklós, Zoltán Toroczkai

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Many real-world networks exhibit correlations between the node degrees. For instance, in socialnetworks nodes tend to connect to nodes of similar degree and conversely, in biological and technological networks, high-degree nodes tend to be linked with low-degree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints.Wepresent a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an exact method to construct and sample graphs with a specified joint-degree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithmis ⊙(NM)whereNis the number of nodes andMis the number of edges.

Original languageEnglish
Article number083052
JournalNew Journal of Physics
Volume17
Issue number8
DOIs
Publication statusPublished - Aug 26 2015

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Keywords

  • algorithm
  • complex networks
  • correlations
  • joint-degree matrix
  • sampling

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Exact sampling of graphs with prescribed degree correlations. / Bassler, Kevin E.; Genio, Charo I Del; Erds, Péter L.; Miklós, I.; Toroczkai, Zoltán.

In: New Journal of Physics, Vol. 17, No. 8, 083052, 26.08.2015.

Research output: Contribution to journalArticle

Bassler, Kevin E. ; Genio, Charo I Del ; Erds, Péter L. ; Miklós, I. ; Toroczkai, Zoltán. / Exact sampling of graphs with prescribed degree correlations. In: New Journal of Physics. 2015 ; Vol. 17, No. 8.
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