Diffusion Centrality in Interconnected Networks

Abstract

The identification of influential or vulnerable nodes in a network is garnering considerable attention nowadays owing to the recent increase in the connectedness of society. Further, knowledge of the properties of interconnected networks is fundamental because of its viable application to the understanding of modular structures that often appear in real-world networks. In this paper, we focus on analysis of centrality, which is defined as the relative importance of a node in a network, and its effect on the probabilistic diffusion dynamics in interconnected networks. We propose a numerical framework in which the importance of the type of the centrality changes along with the diffusion regimes. It is well known that a critical point exists that, when crossed by the infection rate, results in epidemics [1,2]. During the subcritical regime where the infection rate is below the critical point and no epidemics occur, the nodes with the highest number of infections (vulnerable nodes) can be indicated by the alpha centrality, which can be approximated by the degree centrality when the infection rate is almost zero, and the eigenvector centrality when the infection rate approaches the critical point. This theory is examined in numerous simulations using several types of interconnected network. The simulation results fit the estimation of our numerical framework in a small toy network during the subcritical regime. However, interconnection between some networks and the complexity of a network reduce the accuracy of our approximation of the numerical framework, as predicted by our numerical frameworks. Our simulation results also imply that during the critical regime when the infection rate is around the critical point, the type of centrality that can indicate the vulnerable nodes differ according to the topology of the network. In addition, during the supercritical regime, in which the infection rate is sufficiently large, the importance of centrality cannot be discriminated because the number of infections on each node becomes almost the same.