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arXiv · 2301.07959

Belief propagation on networks with cliques and chordless cycles

Peter Mann·Simon Dobson
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Abstract

It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{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.

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Peter Mann, Simon Dobson. 2023-01-19. Belief propagation on networks with cliques and chordless cycles. https://doi.org/10.1103/physreve.107.054303

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