Belief propagation on networks with cliques and chordless cycles

Peter Stephen Mann*, Simon Andrew Dobson

*Corresponding author for this work

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It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, et al. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif based theory would be superior to a tree one; since additional neighbour correlations are encapsulated in the motif structure. In this paper we examine bond percolation on random and real world networks using belief propagation in conjunction with edge-disjoint motif covers. We derive exact message passing expressions for cliques and chordless cycles of finite size. Our theoretical model gives good agreement with Monte Carlo simulation and offers a simple, yet substantial improvement on traditional message passing showing that this approach is suitable to study the properties of random and empirical networks.
Original languageEnglish
Article number054303
Number of pages13
JournalPhysical Review E
Early online date8 May 2023
Publication statusPublished - 8 May 2023


  • Complex networks
  • Belief propagation
  • Clustering


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