Detecting communities in directed acyclic networks using modified LPA algorithms
Networks (or graphs) appear as dominant structures in different domains, including sociology, biology, neuroscience and computing. In most cases, these graphs are directed which changes the semantics of the edges that are no longer symmetrical in the sense that the beginning vertex transfers some property or value to the end vertex, but not vice versa. Detecting community structure in complex networks is an interdisciplinary topic with many relevant areas of application. In order to detect communities in directed acyclic networks, apart from the direction of the edge, the requirement for topological ordering of the vertices should be taken into account. In other words, if the vertices are topologically order is such a way that x1 < x2 < ... < xn we are interested in dividing the network into communities C1, C2, ..., Ck in such a way that: if xi < xj , xi ∈ Ci, xj ∈ Cj then Ci < Cj or Ci = Cj We present an algorithm derived from LPA algorithms which are commonly used in network detection, mostly because of their quick computational time and fairly good results. They were originally developed for undirected networks, but have been modified for this purpose.