Generating Realistic Labelled, Weighted Random Graphs

Michael Charles Davis, Zhanyu Ma, Weiru Liu, Paul Miller, Ruth Hunter, Frank Kee

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
246 Downloads (Pure)


Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.
Original languageEnglish
Pages (from-to)1143-1174
Number of pages32
Issue number4
Early online date8 Dec 2015
Publication statusPublished - Dec 2015

Structured keywords

  • Jean Golding


  • network models
  • generative algorithms
  • random graphs
  • labelled graphs
  • weighted graphs
  • bayesian estimation
  • maximum likelihood estimation
  • beta distribution
  • mixture modeling
  • variational inference


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