Dynamical Influence of Nodes Revisited: A Markov Chain Analysis of Epidemic Process on Networks
LI Ping1,2**, ZHANG Jie3**, XU Xiao-Ke4,5, SMALL Michael6**
1Center for Networked Systems, School of Computer Science, Southwest Petroleum University, Chengdu 610500 2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500 3Center for Computational Systems Biology, Fudan University, Shanghai 200433 4Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 5School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520 6School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
Dynamical Influence of Nodes Revisited: A Markov Chain Analysis of Epidemic Process on Networks
LI Ping1,2**, ZHANG Jie3**, XU Xiao-Ke4,5, SMALL Michael6**
1Center for Networked Systems, School of Computer Science, Southwest Petroleum University, Chengdu 610500 2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500 3Center for Computational Systems Biology, Fudan University, Shanghai 200433 4Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 5School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520 6School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
摘要We provide a theoretical analysis of node importance from the perspective of dynamical processes on networks. In particular, using Markov chain analysis of the susceptible-infected-susceptible (SIS) epidemic model on networks, we derive the node importance in terms of dynamical behaviors on network in a theoretical way. It is found that this quantity happens to be the eigenvector centrality under some conditions, which bridges the topological centrality measure of the nodes with the dynamical influence of the nodes for the dynamical process. We furthermore discuss the condition under which the eigenvector centrality is valid for dynamical phenomena on networks.
Abstract：We provide a theoretical analysis of node importance from the perspective of dynamical processes on networks. In particular, using Markov chain analysis of the susceptible-infected-susceptible (SIS) epidemic model on networks, we derive the node importance in terms of dynamical behaviors on network in a theoretical way. It is found that this quantity happens to be the eigenvector centrality under some conditions, which bridges the topological centrality measure of the nodes with the dynamical influence of the nodes for the dynamical process. We furthermore discuss the condition under which the eigenvector centrality is valid for dynamical phenomena on networks.
LI Ping, ZHANG Jie, XU Xiao-Ke, SMALL Michael. Dynamical Influence of Nodes Revisited: A Markov Chain Analysis of Epidemic Process on Networks[J]. 中国物理快报, 2012, 29(4): 48903-048903.
LI Ping, ZHANG Jie, XU Xiao-Ke, SMALL Michael. Dynamical Influence of Nodes Revisited: A Markov Chain Analysis of Epidemic Process on Networks. Chin. Phys. Lett., 2012, 29(4): 48903-048903.
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