Multi-scale Laplacian community detection in heterogeneous networks

Abstract: Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem of complex network theory. By taking advantage of the recent Laplacian Renormalization Group, we scrutinize information diffusion pathways throughout networks to shed further light on this issue. Based on inter-node communicability, our definition provides a clear-cut framework for resolving the multi-scale mesh of structures in complex networks, disentangling their intrinsic arboreal architecture. As it does not consider any topological null-model assumption, the LRG naturally permits the introduction of scale-dependent optimal partitions. Moreover, we demonstrate the existence of a particular class of nodes, called 'metastable' nodes, that switching regions to which they belong at different scales, likely playing a pivotal role in cross-regional communication and, therefore, in managing macroscopic effects of the whole network.