Density centrality: identifying influential nodes based on area density formula

Identifying central nodes in a network is crucial to accelerate or contain the spreading of information such as diseases and rumors. The problem is formulated as follows, given a complex network, which node(s) is (are) the more important ? The idea of centrality was initially introduced in the context of sociology, to look whether there is a relation between the location of an individual in the network and its influence in group processes. Since then, a plethora of centrality measures has emerged over the years and were employed in a multitude of contexts to rank nodes according to their topological importance. Each centrality targets the problem of influence from its own perspective. In this article we introduce a new centrality that takes inspiration from Area density formula to define the density of each node by considering the degree and the distance between two nodes in a neighborhood of order r = 1, 2, 3, etc... To examine the performances of the proposed measure, we conduct our experiments on synthetic as well as real-world networks by comparing the monotonicity, correlation, the network damage caused by deleting important nodes and the spreading capabilities of nodes using the classical Susceptible-Infected-Recovered (SIR) epidemic model. According to the empirical results, the proposed measure can effectively evaluate the importance of nodes. (C) 2018 Elsevier Ltd. All rights reserved.