Belief propagation on networks with cliques and chordless cycles

TL;DR

This paper develops a belief propagation method incorporating motifs like cliques and chordless cycles to improve the analysis of bond percolation in complex networks, surpassing traditional tree-based models.

Contribution

It introduces exact message passing equations for motifs, enhancing the accuracy of network percolation analysis over existing tree-based theories.

Findings

Good agreement with Monte Carlo simulations

Improved accuracy over traditional message passing

Applicable to both random and real-world networks

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.