Density centrality: identifying influential nodes based on area density formula

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.