Belief propagation on networks with cliques and chordless cycles
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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.
Mann , P S & Dobson , S A 2023 , ' Belief propagation on networks with cliques and chordless cycles ' , Physical Review E , vol. 107 , 054303 . https://doi.org/10.1103/PhysRevE.107.054303
Physical Review E
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DescriptionFunding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).
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