Failure analysis of network nodes and edges in scale-free networks

Abstract

In network failure analysis, most studies always tend to pay more attention to the capabilities of nodes and their impact on networks stability, however, few refer to the ability of edge and node pairs and their impact on the networks. In this article, for deterministic networks, different types of nodes and edges are analyzed, and their differences in location are considered by their contributions to the networks. Then the relative capacity of the flow for edges is proposed, and a quantitative description of scale of failure is explored to analyze the importance rank of network elements. Finally, a numerical example is used to illustrate the proposed method. The results show that single-to-multiple networks always perform well, no matter if we consider the distribution of edges importance, or the difference in scale of failure caused by different nodes.