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-ε approximation for selecting a target set of size k.
KeywordsGreedy Algorithm Success Probability Active Node Threshold Model Cascade Model
Unable to display preview. Download preview PDF.
- 2.Domingos, P., Richardson, M.: Mining the network value of customers. In: Proc. 7th Intl. Conf. on Knowledge Discovery and Data Mining, pp. 57–66 (2001)Google Scholar
- 3.Goldenberg, J., Libai, B., Muller, E.: Using complex systems analysis to advance marketing theory development: Modeling heterogeneity effects on new product growth through stochastic cellular automata. Academy of Marketing Science Review (2001)Google Scholar
- 5.Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: Proc. 8th Intl. Conf. on Knowledge Discovery and Data Mining, pp. 61–70 (2002)Google Scholar
- 6.Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence in a social network. In: Proc. 9th Intl. Conf. on Knowledge Discovery and Data Mining, pp. 137–146 (2003)Google Scholar
- 7.Rogers, E.: Diffusion of innovations, 4th edn. Free Press (1995)Google Scholar
- 8.Valente, T.: Network Models of the Diffusion of Innovations. Hampton Press (1995)Google Scholar
- 9.Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press (1994)Google Scholar
- 13.Peleg, D.: Local majority voting, small coalitions, and controlling monopolies in graphs: A review. In: 3rd Colloquium on Structural Information and Communication, pp. 170–179 (1996)Google Scholar
- 18.Schelling, T.: Micromotives and Macrobehavior. Norton (1978)Google Scholar
- 19.Watts, D.: A simple model of fads and cascading failures. Technical Report 00-12-062, Santa Fe Institute Working Paper (2000)Google Scholar
- 20.Young, H.P.: Individual Strategy and Social Structure: An Evolutionary Theory of Institutions. Princeton University Press, Princeton (1998)Google Scholar
- 21.Young, H.P.: The diffusion of innovations in social networks. Technical Report 02-14-018, Santa Fe Institute Working Paper (2002)Google Scholar