Finding Critical Nodes for Inhibiting Diffusion of Complex Contagions in Social Networks

We study the problem of inhibiting diffusion of complex contagions such as rumors, undesirable fads and mob behavior in social networks by removing a small number of nodes (called critical nodes) from the network. We show that, in general, for any ρ ≥ 1, even obtaining a ρ-approximate solution to these problems is NP-hard. We develop efficient heuristics for these problems and carry out an empirical study of their performance on three well known social networks, namely epinions, wikipedia and slashdot. Our results show that the heuristics perform well on the three social networks.

[1]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[2]  Stephen P. Borgatti,et al.  Identifying sets of key players in a social network , 2006, Comput. Math. Organ. Theory.

[3]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

[4]  Krishna P. Gummadi,et al.  Characterizing social cascades in flickr , 2008, WOSN '08.

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

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

[7]  Andreas Krause,et al.  Cost-effective outbreak detection in networks , 2007, KDD '07.

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

[9]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[10]  Ramanathan V. Guha,et al.  Propagation of trust and distrust , 2004, WWW '04.

[11]  Panos M. Pardalos,et al.  Detecting critical nodes in sparse graphs , 2009, Comput. Oper. Res..

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

[13]  Matthew Richardson,et al.  Mining knowledge-sharing sites for viral marketing , 2002, KDD.

[14]  Ramanathan V. Guha,et al.  Information diffusion through blogspace , 2004, WWW '04.

[15]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

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

[17]  Harry B. Hunt,et al.  Complexity of reachability problems for finite discrete dynamical systems , 2006, J. Comput. Syst. Sci..

[18]  J. Kleinberg.  Algorithmic Game Theory: Cascading Behavior in Networks: Algorithmic and Economic Issues , 2007 .

[19]  M. Macy,et al.  Complex Contagions and the Weakness of Long Ties1 , 2007, American Journal of Sociology.

[20]  Aravind Srinivasan,et al.  Structure of Social Contact Networks and Their Impact on Epidemics , 2004, Discrete Methods in Epidemiology.

[21]  Tanya Y. Berger-Wolf,et al.  A framework for community identification in dynamic social networks , 2007, KDD '07.

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

[23]  Jure Leskovec,et al.  The dynamics of viral marketing , 2005, EC '06.

[24]  Graham Cormode,et al.  Discrete methods in epidemiology , 2007 .

[25]  Fred S. Roberts,et al.  Irreversible k-threshold processes: Graph-theoretical threshold models of the spread of disease and of opinion , 2009, Discret. Appl. Math..

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

[27]  Jon M. Kleinberg,et al.  The structure of information pathways in a social communication network , 2008, KDD.

[28]  J. Kleinberg,et al.  Networks, Crowds, and Markets , 2010 .

[29]  Tanya Y. Berger-Wolf,et al.  Finding Spread Blockers in Dynamic Networks , 2008, SNAKDD.

[30]  John Mylopoulos,et al.  The Semantic Web - ISWC 2003 , 2003, Lecture Notes in Computer Science.

[31]  Spain,et al.  Cascade Dynamics of Complex Propagation , 2005, physics/0504165.