Community detection of weighted complex networks via transitive closure

The K-means algorithm has been successfully applied to many complex network analysis problems. However, this method is sensitive to how the first cluster centers are chosen. It is possible to minimize superfluous runs by choosing the first cluster center in advance because each run produces a unique set of results. To overcome this issue, an algorithm for Community Detection based on Transitive Closure (CoDTC) has been introduced. In this algorithm, the initial cluster center is provided by degree centrality and T-transitive closure. The algorithm initializes with the calculation of the similarity relation matrix. Then, to avoid the limitation of sparse problems in complex network analysis, we offer the idea of transitive closure on weighted networks to solve the sparsity issue. This notion is based on imposing a t-norm inequality on the connection weights and providing a method to compute them. Finally, based on T-transitive closure, new cluster centers are calculated iteratively to avoid random selection of cluster centers. In this paper, we demonstrate the efficacy of the CoDTC approach on a diverse range of real and artificial networks, encompassing both big and small communities.