Locating influential nodes in complex networks

Understanding and controlling spreading processes in networks is an important topic with many diverse applications, including information dissemination, disease propagation and viral marketing. It is of crucial importance to identify which entities act as influential spreaders that can propagate information to a large portion of the network, in order to ensure efficient information diffusion, optimize available resources or even control the spreading. In this work, we capitalize on the properties of the K-truss decomposition, a triangle-based extension of the core decomposition of graphs, to locate individual influential nodes. Our analysis on real networks indicates that the nodes belonging to the maximal K-truss subgraph show better spreading behavior compared to previously used importance criteria, including node degree and k-core index, leading to faster and wider epidemic spreading. We further show that nodes belonging to such dense subgraphs, dominate the small set of nodes that achieve the optimal spreading in the network.

[1]  Matthew Richardson,et al.  Trust Management for the Semantic Web , 2003, SEMWEB.

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

[3]  Yiping Yao,et al.  Identifying all-around nodes for spreading dynamics in complex networks , 2012 .

[4]  Matthew Richardson,et al.  Mining the network value of customers , 2001, KDD '01.

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

[6]  Jia Wang,et al.  Truss Decomposition in Massive Networks , 2012, Proc. VLDB Endow..

[7]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[8]  Hernán A. Makse,et al.  Influence maximization in complex networks through optimal percolation , 2015, Nature.

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

[10]  Hui Gao,et al.  Identifying Influential Nodes in Large-Scale Directed Networks: The Role of Clustering , 2013, PloS one.

[11]  Krishna P. Gummadi,et al.  On the evolution of user interaction in Facebook , 2009, WOSN '09.

[12]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[13]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

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

[15]  Yuval Shavitt,et al.  A model of Internet topology using k-shell decomposition , 2007, Proceedings of the National Academy of Sciences.

[16]  Éva Tardos,et al.  Influential Nodes in a Diffusion Model for Social Networks , 2005, ICALP.

[17]  Zhiming Zheng,et al.  Searching for superspreaders of information in real-world social media , 2014, Scientific Reports.

[18]  Han Zhao,et al.  Identifying influential nodes in complex networks with community structure , 2013, Knowl. Based Syst..

[19]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[20]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[21]  Jure Leskovec,et al.  {SNAP Datasets}: {Stanford} Large Network Dataset Collection , 2014 .

[22]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[23]  Yamir Moreno,et al.  Locating privileged spreaders on an online social network. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Leland L. Beck,et al.  Smallest-last ordering and clustering and graph coloring algorithms , 1983, JACM.

[25]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[26]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

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

[28]  Vladimir Batagelj,et al.  An O(m) Algorithm for Cores Decomposition of Networks , 2003, ArXiv.

[29]  Jon Kleinberg,et al.  Maximizing the spread of influence through a social network , 2003, KDD '03.

[30]  Yi-Cheng Zhang,et al.  Leaders in Social Networks, the Delicious Case , 2011, PloS one.

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

[32]  Jure Leskovec,et al.  Predicting positive and negative links in online social networks , 2010, WWW '10.

[33]  Duanbing Chen,et al.  Path diversity improves the identification of influential spreaders , 2013, ArXiv.

[34]  Christos Faloutsos,et al.  Epidemic thresholds in real networks , 2008, TSEC.

[35]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[36]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

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

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

[39]  Stephen B. Seidman,et al.  Network structure and minimum degree , 1983 .

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

[41]  K. Pauwels,et al.  Effects of Word-of-Mouth versus Traditional Marketing: Findings from an Internet Social Networking Site , 2009 .

[42]  Duanbing Chen,et al.  Identifying Influential Spreaders by Weighted LeaderRank , 2013, ArXiv.

[43]  Srinivasan Parthasarathy,et al.  Extracting Analyzing and Visualizing Triangle K-Core Motifs within Networks , 2012, 2012 IEEE 28th International Conference on Data Engineering.

[44]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[45]  ZhaoHan,et al.  Identifying influential nodes in complex networks with community structure , 2013 .

[46]  Leandros Tassiulas,et al.  Detecting Influential Spreaders in Complex, Dynamic Networks , 2013, Computer.

[47]  Yiming Yang,et al.  The Enron Corpus: A New Dataset for Email Classi(cid:12)cation Research , 2004 .