Soft unveiling of communities via egonet tensors

The task of community detection over a network pertains to identifying the underlying groups of nodes whose often-hidden association has manifested itself in dense connections among the members, and sparse inter-community links. The present work aims at improving the robustness of the traditional matrix-based community detection algorithms via capturing multi-hop connectivity patterns through tensor analysis. To this end, a novel tensor-based network representation is advocated in this contribution, and the task of community detection is cast as a constrained PARAFAC decomposition. Subsequently, the proposed tri-linear minimization is handled via alternating least-squares, where intermediate subproblems are solved using the alternating direction method of multipliers (ADMM) to ensure convergence. The framework is further broadened to accommodate time-varying graphs, where the edgeset as well as the underlying communities evolve through time. Numerical tests corroborate the increased robustness provided through the novel representation as well as the proposed tensor decomposition.