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Mathematical Problems in Engineering
Volume 2015, Article ID 752893, 7 pages
Research Article

Threshold for the Outbreak of Cascading Failures in Degree-Degree Uncorrelated Networks

1College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
2School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China
3College of Electrical and Information Engineering, Hunan University, Changsha 410015, China
4School of Information and Electric Engineering, Zhejiang University City College, Hangzhou 310015, China

Received 26 June 2015; Accepted 26 November 2015

Academic Editor: Xiaobo Qu

Copyright © 2015 Junbiao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In complex networks, the size of the giant component formed by unfailed nodes is critically important for estimating the robustness of networks against cascading failures. In order to explore the critical moment of cascading failures break-out, we provide a cascade of overload failure model with local load sharing mechanism and then deduce the threshold of node capacity when the large-scale cascading failures happen and unfailed nodes in steady state cannot connect to each other to form a large connected subnetwork. We get the theoretical derivation of this threshold in degree-degree uncorrelated networks and validate the effectiveness of this method in simulation. This threshold provides us with a guidance to improve the network robustness under the premise of limited capacity resource when creating a network and assigning load. Therefore, this threshold is useful and important to analyze the robustness of networks. We believe that our research provides us with a guidance to improve the network robustness under the premise of limited capacity resource.