Background¶
We present multimodbp, a belief propagation implementation of multilayer modularity for communtiy detectionOur tool is a C++ based implentation of the belief propagation algorithm (also called the sum-product or message passing algorithm) wrapped in Python for convenient access and execution.
Introduction: Belief Propagation¶
Modularity¶
Multilayer Modularity¶
One of the strengths of modularity is that it has been extended in a principled way into a variety of network topologies in particular the multilayer context. The multilayer formulation [1] for modularity incorporates the interlayer connectivity of the network in the form of a second adjacency matrix \(C_{ij}\)
Communities in this context group nodes within the layers and across the layers. The inclusion of the \(C_ij\) boost the modularity for communites that include alot interlayer links. There is an additional parameter, \(\omega\) that tunes how much weight these interlink ties contribute to the modularity.