Influential Nodes in a Diffusion Model for Social Networks

We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of “word-of-mouth” referral. Our work builds on the observation that individuals’ decisions to purchase a product or adopt an innovation are strongly influenced by recommendations from their friends and acquaintances. Understanding and leveraging this influence may thus lead to a much larger spread of the innovation than the traditional view of marketing to individuals in isolation. In this paper, we define a natural and general model of influence propagation that we term the decreasing cascade model, generalizing models used in the sociology and economics communities. In this model, as in related ones, a behavior spreads in a cascading fashion according to a probabilistic rule, beginning with a set of initially “active” nodes. We study the target set selection problem: we wish to choose a set of individuals to target for initial activation, such that the cascade beginning with this active set is as large as possible in expectation. We show that in the decreasing cascade model, a natural greedy algorithm is a 1-1/ e-e approximation for selecting a target set of size k.

[1]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

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

[3]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[4]  T. Schelling.  Micromotives and Macrobehavior , 1978 .

[5]  Peter H. Reingen,et al.  Social Ties and Word-of-Mouth Referral Behavior , 1987 .

[6]  John Scott.  What is social network analysis , 2010 .

[7]  M. Macy.  Chains of Cooperation: Threshold Effects in Collective Action , 1991 .

[8]  S. Wasserman,et al.  Social Network Analysis: Computer Programs , 1994 .

[9]  Thomas W. Valente.  Network models of the diffusion of innovations , 1996, Comput. Math. Organ. Theory.

[10]  D. Peleg.  Local Majority Voting, Small Coalitions and Controlling Monopolies in Graphs: A Review , 1996 .

[11]  H. Young,et al.  Individual Strategy and Social Structure: An Evolutionary Theory of Institutions , 1999 .

[12]  Duncan J. Watts,et al.  A Simple Model of Fads and Cascading Failures on Sparse Switching Networks , 2000 .

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

[14]  Eli Berger.  Dynamic Monopolies of Constant Size , 2001, J. Comb. Theory, Ser. B.

[15]  Jacob Goldenberg,et al.  Using Complex Systems Analysis to Advance Marketing Theory Development , 2001 .

[16]  Jacob Goldenberg,et al.  Talk of the Network: A Complex Systems Look at the Underlying Process of Word-of-Mouth , 2001 .

[17]  Eyton,et al.  The Diffusion of Innovations in Social Networks , 2002 .

[18]  M. Macy,et al.  FROM FACTORS TO ACTORS: Computational Sociology and Agent-Based Modeling , 2002 .

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

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

[21]  E. Rogers,et al.  Diffusion of innovations , 1964, Encyclopedia of Sport Management.