Applications of Discrete Dirichlet Problem to Semi-supervised Community Detection by Label Propagation

We propose a new version of an algorithm based on Dirichlet boundary for community detection under the assumption of partially pre-labelled community members. We present a complete mathematical derivation of this method from the continuous Dirichlet boundary problem making explicit various assumptions underlying its discretization. We show, based on this derivation, how our algorithm differs from the ones previously derived in this spirit. Via a set of experiments we demonstrate how this new algorithm works for several benchmark data sets.