Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs

Understand

We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.).

• Each vertex in these networks belongs to a given set of motifs (generalization of the configuration model).
• These networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs.
• Here a hypergraph is a generalization of a graph, where a hyperedge can connect any number of vertices.