| CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
|
|
|
|
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 |
|
| Cite this article: |
|
LI Ping, ZHANG Jie, XU Xiao-Ke et al 2012 Chin. Phys. Lett. 29 048903 |
|
|
|
|
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.
|
|
|
Received: 11 January 2012
Published: 04 April 2012
|
|
| PACS: |
89.75.Hc
|
(Networks and genealogical trees)
|
| |
89.75.Fb
|
(Structures and organization in complex systems)
|
|
|
|
|
|
| [1] Wasserman S 1994 Social Network Analysis: Methods and Applications (Cambridge: Cambridage University)[2] Watts D J and Dodds P S 2007 J. Consumer Res. 34 441[3] Zhuo Z, Cai S M, Fu Z Q and Zhang J 2011 Phys. Rev. E 84 031923[4] Zhang J, Zhou C, Xu X and Small M 2010 Phys. Rev. E 82 026116[5] Crucitti P, Latora V and Marchiori M 2004 Phys. Rev. E 69 045104[6] Yan G, Zhou T, Hu B, Fu Z Q and Wang B H 2006 Phys. Rev. E 73 046108[7] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E and Makse H A 2010 Nature Phys. 6 888[8] Klemm K, Serrano M, Eguiluz V M and Miguel M S 2012 Sci. Rep. 2 292[9] Masuda N, Kawamura Y and Kori H 2009 Phys. Rev. E 80 046114[10] Masuda N and Kori H 2010 Phys. Rev. E 82 056107[11] Zhang J, Xu X K, Li P, Zhang K and Small M 2011 Chaos 21 016107[12] Katz L 1953 Psychometrika 18 39[13] Freeman L C 1979 Social networks 1 215[14] Bonacich P 1972 J. Math. Sociol. 2 113[15] Bonacich P 2007 Social Networks 29 555[16] Lohmann G, Margulies D S, Horstmann A, Pleger B, Lepsien J, Goldhahn D, Schloegl H, Stumvoll M, Villringer A and Turner R 2010 PloS one 5 e10232[17] Özgür A, Vu T, Erkan G and Radev D R 2008 Bioinformatics 24 i277[18] Jing Y and Baluja S 2008 Proceeding of the 17th International Conference on World Wide Web (New York, USA 21–25 April 2008) p 307[19] Ganguly N and Kharagpur I I T 2006 IMSc Workshop on Modeling Infectious Diseases (Chennai, India 4–6 September 2006)[20] Moreno Y, Pastor Satorras R and Vespignani A 2002 Eur. Phys. J. B 26 521[21] Moreno Y, Nekovee M and Pacheco A F 2004 Phys. Rev. E 69 066130[22] Zhou T, Fu Z Q and Wang B H 2005 Prog. Nat. Sci. 16 12[23] Zhang H, Zhang J, Zhou C, Small M and Wang B 2010 New J. Phys. 12 023015[24] G ómez S, Arenas A, Borge Holthoefer J, Meloni S and Moreno Y 2010 Europhys. Lett. 89 38009[25] Wang Y, Chakrabarti D, Wang C and Faloutsos C 2003 22nd International Symposium on Reliable Distributed Systems (Florence, Italy 6–8 October 2003) p 25[26] Gómez Gardeñes J and Moreno Y 2006 Phys. Rev. E 73 056124[27] Hu H B and Wang X F 2008 Physica A 387 3769[28] Farkas I J, Derenyi I, Barabasi A L and Vicsek T 2001 Phys. Rev. E 64 026704 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
