Community structure in networks: Girvan-Newman algorithm improvement

Real world networks often have community structure. It is characteristic that the groups of nodes are connected denser within themselves and rarely with each other. The Girvan-Newman method for the detection and analysis of community structure is based on the iterative elimination of edges with the highest number of the shortest paths that go through them. By eliminating edges the network breaks down into smaller networks, i.e. communities. This paper introduces improved Girvan-Newman method where multi-edge removal is allowed, and presents the results of the application of both methods to the existing real social network (Zachary karate club), the computergenerated network and the tumor genes and their mutations network. The improved algorithm in practice reduces the number of operations, but retains the same computational complexity, so it cannot be applied to networks with a very large number of nodes. The most important feature of our improvement is that the result is graph-theoretical invariant, while original algorithm depends on the vertex labeling.