Resistance and Security Index of Networks: Structural Information Perspective of Network Security

Recently, Li and Pan defined the metric of the K-dimensional structure entropy of a structured noisy dataset G to be the information that controls the formation of the K-dimensional structure T of G that is evolved by the rules, order and laws of G, excluding the random variations that occur in G. Here, we propose the notion of resistance of networks based on the one- and two-dimensional structural information of graphs. Given a graph G, we define the resistance of G, written (G), as the greatest overall number of bits required to determine the code of the module that is accessible via random walks with stationary distribution in G, from which the random walks cannot escape. We show that the resistance of networks follows the resistance law of networks, that is, for a network G, the resistance of G is (G)=ℋ¹(G) - ℋ²(G), where ℋ¹(G) and ℋ²(G) are the one- and two-dimensional structure entropies of G, respectively. Based on the resistance law, we define the security index of a network G to be the normalised resistance of G, that is, ρ(G) = 1 - ℋ²(G)/ℋ¹(G). We show that the resistance and security index are both well-defined measures for the security of the networks.