Effect of rich-club on diffusion in complex networks

One of the main issues in complex networks is the phenomenon of diffusion in which the goal is to find the nodes with the highest diffusing power. In diffusion, there is always a conflict between accuracy and efficiency time complexity; therefore, most of the recent studies have focused on finding new centralities to solve this problem and have offered new ones, but our approach is different. Using one of the complex networks’ features, namely the “rich-club”, its effect on diffusion in complex networks has been analyzed and it is demonstrated that in datasets which have a high rich-club, it is better to use the degree centrality for finding influential nodes because it has a linear time complexity and uses the local information; however, this rule does not apply to datasets which have a low rich-club. Next, real and artificial datasets with the high rich-club have been used in which degree centrality has been compared to famous centrality using the SIR standard.

[1]  André A Moreira,et al.  Biased percolation on scale-free networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Phillip Bonacich,et al.  Eigenvector-like measures of centrality for asymmetric relations , 2001, Soc. Networks.

[3]  Qiang Guo,et al.  Ranking the spreading influence in complex networks , 2013, ArXiv.

[4]  Mikko Kivelä,et al.  Generalizations of the clustering coefficient to weighted complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Santo Fortunato,et al.  Community detection in networks: A user guide , 2016, ArXiv.

[6]  M. Kuperman,et al.  Small world effect in an epidemiological model. , 2000, Physical review letters.

[7]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[8]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.

[9]  Luciano da Fontoura Costa,et al.  Rich-club phenomenon across complex network hierarchies , 2007 .

[10]  Piraveenan Mahendra,et al.  Node Assortativity in Complex Networks: An Alternative Approach , 2014, ICCS.

[11]  Yi Pan,et al.  Identification of Essential Proteins Based on Edge Clustering Coefficient , 2012, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[12]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[13]  Marián Boguñá,et al.  Popularity versus similarity in growing networks , 2011, Nature.

[14]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[15]  Timothy Ravasi,et al.  From link-prediction in brain connectomes and protein interactomes to the local-community-paradigm in complex networks , 2013, Scientific Reports.

[16]  Weiren Shi,et al.  Evaluating the importance of nodes in complex networks , 2016 .

[17]  A Díaz-Guilera,et al.  Self-similar community structure in a network of human interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[20]  Pablo M. Gleiser,et al.  Community Structure in Jazz , 2003, Adv. Complex Syst..

[21]  Yicheng Zhang,et al.  Identifying influential nodes in complex networks , 2012 .

[22]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[23]  Zonghua Liu,et al.  An alternative approach to characterize the topology of complex networks and its application in epidemic spreading , 2009, Frontiers of Computer Science in China.

[24]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[25]  Sergey Brin,et al.  Reprint of: The anatomy of a large-scale hypertextual web search engine , 2012, Comput. Networks.

[26]  Alessandro Vespignani,et al.  Detecting rich-club ordering in complex networks , 2006, physics/0602134.

[27]  Hernán A. Makse,et al.  Spreading dynamics in complex networks , 2013, ArXiv.

[28]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[29]  Zhi-Gang Shao,et al.  Blackmail propagation on small-world networks , 2005 .

[30]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Mohammad Ali Nematbakhsh,et al.  IMPROVING DETECTION OF INFLUENTIAL NODES IN COMPLEX NETWORKS , 2015, ArXiv.

[32]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[33]  Attila Korösi,et al.  Geometric explanation of the rich-club phenomenon in complex networks , 2017, Scientific Reports.

[34]  Renana Peres,et al.  The impact of network characteristics on the diffusion of innovations , 2014 .

[35]  M. Newman.  Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[37]  Harry Eugene Stanley,et al.  Correlation between centrality metrics and their application to the opinion model , 2014, The European Physical Journal B.

[38]  An Zeng,et al.  Ranking spreaders by decomposing complex networks , 2012, ArXiv.

[39]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[41]  Claudio Castellano,et al.  Thresholds for epidemic spreading in networks , 2010, Physical review letters.

[42]  Paul J. Laurienti,et al.  A New Measure of Centrality for Brain Networks , 2010, PloS one.

[43]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[45]  Sangwook Kim,et al.  Identifying and ranking influential spreaders in complex networks by neighborhood coreness , 2014 .

[46]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[47]  Xiaofan Wang,et al.  Unified index to quantifying heterogeneity of complex networks , 2008 .

[48]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[49]  Duanbing Chen,et al.  Vital nodes identification in complex networks , 2016, ArXiv.

[50]  M. Kendall.  A NEW MEASURE OF RANK CORRELATION , 1938 .

[51]  Shi Zhou,et al.  The rich-club phenomenon in the Internet topology , 2003, IEEE Communications Letters.