Alternating between consensus and leader selection reveals community structure in networks

Abstract

In this paper, we propose two novel algorithms to detect community structure in networks based on consensus dynamics. The first algorithm identifies the communities in networks by alternating between recognizing leader nodes following the analysis of influence coefficients of nodes, and finding the nodes belonging to the groups of their corresponding leader nodes using consensus dynamics and the difference coefficients of nodes. The second algorithm is an extension to the first one via the leader-following models. After confirming the leader nodes according to the first algorithm, we reveal the memberships of nodes belonging to the corresponding leaders by performing consensus dynamics. In the second algorithm, an approach to calculating the memberships of nodes is proposed. The corresponding leader nodes of communities can be confirmed naturally and the status of nodes in networks can be determined quantitatively. Finally, our algorithms are applied to real-world and computer generated networks whose community structures are well known. The experiment results show the effectiveness and reliability of the proposed algorithms.