Community detection algorithms help us improve the management of complex networks and provide a clean sight of them. We can encounter complex networks in various fields such as social media, bioinformatics, recommendation systems, and search engines. As the definition of the community changes based on the problem considered, there is no algorithm that works universally for all kinds of data and network structures. Communities can be disjointed such that each member is in at most one community or overlapping such that every member is in at least one community. In this study, we examine the problem of finding overlapping communities in complex networks and propose a new algorithm based on the similarity of neighbors. This algorithm runs in O(mlgm) running time in the complex network containing m number of relationships. To compare our algorithm with existing ones, we select the most successful four algorithms from the Community Detection library (CDlib) by eliminating the algorithms that require prior knowledge, are unstable, and are time-consuming. We evaluate the successes of the proposed algorithm and the selected algorithms using various known metrics such as modularity, F-score, and Normalized Mutual Information. In addition, we adapt the coverage metric defined for disjoint communities to overlapping communities and also make comparisons with this metric. We also test all of the algorithms on small graphs of real communities. The experimental results show that the proposed algorithm is successful in finding overlapping communities.
We investigate the control of dynamical networks for the case of nodes, that although different, can be make passive by feedback. The so-called V-stability characterization allows for a simple set of stabilization conditions even in the case of nonidentical nodes. This is due to the fact that under V-stability characterization the dynamical difference between node of a network reduces to their different passivity degrees, that is, a measure of the required feedback gain necessary to make the node stable at a desired solution. We propose a pinning control strategy that extends this approach to solve the tracking problem, furthermore using an adaptive controller approach we provide a methodology to impose a common reference trajectory to a network of different nodes by pinning only a few of them to the desired solution. We illustrate our results with numerical simulation of well-known benchmark systems.
In this paper, we investigate the finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. We propose new adaptive controllers, with which we can synchronize two complex dynamical networks within finite time. Sufficient conditions for the finite-time adaptive outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical results.