Modelling cascading failures in networks with the harmonic closeness

Abstract

Many studies on cascading failures adopt the degree or the betweenness of a node to define its load. From a novel perspective, we propose an approach to obtain initial loads considering the harmonic closeness and the impact of neighboring nodes. Based on simulation results for different adjustable parameter θ, local parameter δ and proportion of attacked nodes f, it is found that in scale-free networks (SF networks), small-world networks (SW networks) and Erdos-Renyi networks (ER networks), there exists a negative correlation between optimal θ and δ. By the removal of the low load node, cascading failures are more likely to occur in some cases. In addition, we find a valuable result that our method yields better performance compared with other methods in SF networks with an arbitrary f, SW and ER networks with large f. Moreover, the method concerning the harmonic closeness makes these three model networks more robust for different average degrees. Finally, we perform the simulations on twenty real networks, whose results verify that our method is also effective to distribute the initial load in different real networks.

A Comprehensive Analysis of Robustness in Interdependent Mechatronic Systems under Attack Strategies

“…As a result of the impact of cascading failures, Motter et al developed a cascading model where the load on the node is dependent on the total number of shortest paths passing through it [13,14]. Additionally, the degree [15,16], the betweenness [17], and the harmonic closeness [18,19], as metrics of nodes to quantify their characteristics, have been widely adopted to obtain the load. Similarly, in order to define the cascading failure model concerning the edge, these measures have also been further studied [20][21][22][23][24].…”

“…Similarly, in order to define the cascading failure model concerning the edge, these measures have also been further studied [20][21][22][23][24]. On the basis of the comparison of different definitions of the load, Hao et al found that the networks where the loads on the node and edge are defined as the harmonic closeness have a higher level of robustness [18,19,24]. Different from the cascading failure induced by overloads, Newman et al employed the generating function formalism to study the failure process of nodes and edges by means of percolation theory from another perspective [25].…”