Application of the differential equations method for identifying communities in sparse networks

In our previous work a new method of identifying communities in networks was presented. The method is based on a time evolution of the network according to a set of differential equations. It was applied to networks consisting of fully connected sub-networks. However, networks describing real systems are often sparse. Here the method is applied to sparse networks. The results are compared with those of an agglomerative hierarchical method based on modularity maximisation proposed by Newman and a divisive method proposed by Duch and Arenas based also on optimisation of the modularity. Obtained results show that the differential equation method usually works better than two remaining methods, allowing for more appropriate identification of the network structure.