[1] J Kostka and Y Oswald.... Word of mouth: Rumor dissemination in social networks. STRUCTURAL INFORMATION AND COMMUNICATION COMPLEXITY, Jan 2008. [ bib | .pdf ]
A. Shvartsman and P. Felber (Eds.): , LNCS 5058, pp. 185-196, . c Springer-Verlag Berlin Heidelberg Page 2. 186 J. Kostka, YA , and R. Wattenhofer of players can choose different starting nodes in a graph to spread messages.

[2] J.-C Bermond, J Bond, D Peleg, and S Perennes. The power of small coalitions in graphs. Discrete Applied Mathematics, 127(3), May 2003. [ bib | http ]
This paper considers the question of the influence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a general graph. Say that a vertex v is controlled by the coalition M if the majority ...

[3] Marc Lelarge. Diffusion of innovations on random networks: Understanding the chasm. WINE '08: Proceedings of the 4th International Workshop on Internet and Network Economics, Dec 2008. [ bib | http ]
We analyze diffusion models on sparse random networks with neighborhood effects. We show how large cascades can be triggered by small initial shocks and compute critical parameters: contagion threshold for a random network, phase transition in the size ...

[4] Marc Lelarge. Efficient control of epidemics over random networks. SIGMETRICS '09: Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems, Jun 2009. [ bib | http ]
Motivated by the modeling of the spread of viruses or epidemics with coordination among agents, we introduce a new model generalizing both the basic contact model and the bootstrap percolation. We analyze this percolated threshold model when the underlying ...

Keywords: vaccination, epidemics, random graphs
[5] E Mossel and S Roch. Submodularity of influence in social networks: From local to global. SIAM Journal on Computing, Dec 2010. [ bib | http ]
Social networks are often represented as directed graphs, where the nodes are individuals and the edges indicate a form of social relationship. A simple way to model the diffusion of ideas, innovative behavior, or “word-of-mouth” effects on such a graph is to consider an

[6] Maksim Kitsak, Lazaros K Gallos, Shlomo Havlin, Fredrik Liljeros, Lev Muchnik, H Eugene Stanley, and Hernán A Makse. Identification of influential spreaders in complex networks. Nature Physics, 6(11):888-893, Aug 2010. [ bib | DOI | http ]
Nature Physics 6, 888 (2010). doi:10.1038/nphys1746

[7] Dominic Meier, Yvonne Pignolet, Stefan Schmid, and Roger Wattenhofer. On the windfall of friendship: inoculation strategies on social networks. EC '08: Proceedings of the 9th ACM conference on Electronic commerce, Jul 2008. [ bib | http ]
This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network ...

Keywords: windfall of friendship, social networks, virus propagation, equilibria, game theory
[8] E Berger. Dynamic monopolies of constant size. Journal of Combinatorial Theory, Series B, 83(2):191-200, 2001. [ bib ]
[9] D Kempe, Jon Kleinberg, and Eva Tardos. Influential nodes in a diffusion model for social networks. Proceedings of 32nd International Colloquium on Automata, Languages and Programming (ICALP), pages 1127-1138, Jan 2005. [ bib | .pdf ]
Abstract. 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 ...

[10] Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group formation in large social networks: membership, growth, and evolution. KDD '06: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, Aug 2006. [ bib | http ]
The processes by which communities come together, attract new members, and develop over time is a central research issue in the social sciences - political movements, professional organizations, and religious denominations all provide fundamental examples ...

Keywords: on-line communities, diffusion of innovations, social networks
[11] Stephen Morris. Contagion. The Review of Economic Studies, 67(1):57-78, Jan 2000. [ bib | http ]
Each player in an infinite population interacts strategically with a finite subset of that population. Suppose each player's binary choice in each period is a best response to the population choices of the previous period. When can behaviour that is initially played by only a finite set of players spread to the whole population? This paper characterizes when such contagion is possible for arbitrary local interaction systems. Maximal contagion occurs when local interaction is sufficiently uniform and there is low neighbour growth, i.e. the number of players who can be reached in k steps does not grow exponentially in k.

[12] Mark Granovetter. Threshold models of collective behavior. The American Journal of Sociology, 83(6):1420-1443, May 1978. [ bib | http ]
Models of collective behavior are developed for situations where actors have two alternatives and the costs and/or benefits of each depend on how many other actors choose which alternative. The key concept is that of "threshold": the number or proportion of others who must make one decision before a given actor does so; this is the point where net benefits begin to exceed net costs for that particular actor. Beginning with a frequency distribution of thresholds, the models allow calculation of the ultimate or "equilibrium" number making each decision. The stability of equilibrium results against various possible changes in threshold distributions is considered. Stress is placed on the importance of exact distributions distributions for outcomes. Groups with similar average preferences may generate very different results; hence it is hazardous to infer individual dispositions from aggregate outcomes or to assume that behavior was directed by ultimately agreed-upon norms. Suggested applications are to riot behavior, innovation and rumor diffusion, strikes, voting, and migration. Issues of measurement, falsification, and verification are discussed.

[13] Jure Leskovec, Andreas Krause, Carlos Guestrin, Christos Faloutsos, Jeanne VanBriesen, and Natalie Glance. Cost-effective outbreak detection in networks. KDD '07: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, Aug 2007. [ bib | http ]
Given a water distribution network, where should we place sensors toquickly detect contaminants? Or, which blogs should we read to avoid missing important stories?. These seemingly different problems share common structure: Outbreak detection can be ...

Keywords: submodular functions, virus propagation, information cascades, graphs, sensor placement
[14] David Kempe, Jon Kleinberg, and Éva Tardos. Maximizing the spread of influence through a social network. KDD '03: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, Aug 2003. [ bib | http ]
Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies ...

Keywords: approximation algorithms, diffusion of innovations, viral marketing, social networks

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