关键词: 超图/
无标度超网络/
相继故障/
耦合映像格子
English Abstract
Cascading failure analysis in hyper-network based on the hypergraph
Ma Xiu-Juan1,2,Zhao Hai-Xing2,
Hu Feng2
1.School of Computer Science, Shaanxi Normal University, Xi'an 710062, China;
2.School of Computer Science, Qinghai Normal University, Xining 810008, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 61164005), the Chunhui Program of Ministry of Education of China (Grant No. Z2012101), the Project of Qinghai Office of Science and Technology, China (Grant Nos. 2013-Z-Y17, 2015-ZJ-723), the Key Laboratory of Tibetan Information Processing (Qinghai Normal University), Ministry of Education, China, and the Key Laboratory of Tibetan Information Processing and Machine Translation, Qinghai Province, China.Received Date:09 November 2015
Accepted Date:04 January 2016
Published Online:05 April 2016
Abstract:In this paper, we analyze the diffusion patterns of cascading failure, which happen in the express hypernetwork and electronic hypernetwork respectively. The cascading failure of the express hypernetwork is diffused by the node, and the cascading failure of the electronic hypernetwork is diffused by the hyper-edge. According to hyper-graph theory, we propose two methods to characterize these cascading failures, which are 2-section graph analytical method and line-graph analytical method. We analyze the characteristics of the cascading failures based on node by using the 2-section graph analytical method and based on hyper-edge by using line-graph analytical method, respectively. We construct a k uniform scale-free hypernetwork and analyze the cascading failure process of this hypernetwork based on the couple map lattice according to our methods. The simulation results show that the scale-free hypernetworks are both robust and vulnerable for attack. It is found that the cascading failure based on the node of k uniform scale-free hypernetwork is associated with the hyper-degree distribution of nodes, and the scale-free hypernetwork is robust for random attack and vulnerable for deliberate attack. The more nodes a hyper-edge has, the better robustness the hypernetwork has.The cascading failure based on the hyper-edge is different from the cascading failure based on the node. The cascading failure based on the hyper-edge is associated with the hyper-edge degree distribution. The hyper-edge degree distribution of the scale-free hypernetwork is not entirely the power-low distribution. When the cascading failure is diffused by the hyper-edge, the hypernetwork is vulnerable for random attack and robustness for deliberate attack if there are 3 or 5 nodes in a hyper-edge. Moreover, the hypernetwork becomes robust for the random attack if there are 7 nodes in a hyper-edge. Furthermore, the k uniform scale-free hypernetwork is more robust than the same size Barabasi-Albert scale-free network for the same attack. The cascading failure process based on the hyper-edge is slower than based on the node. We find that the edge number is another influential factor of robustness. The network is more robust if it has more edges for fixed node number. The line-graph has more edges than the 2-section graph in the same size scale-free hypernetwork, so the cascading failure of node is slower than that of hyper-edge.
Keywords: hypergraph/
scale-free hypernetwork/
cascading failure/
couple map lattice
