Abstract
In this paper, we introduce homophily to a game-theoretic model of collective action (e.g., protests) on Facebook and study the effect of homophily in individuals’ willingness to participate in collective action, i.e., their thresholds, on the emergence and spread of collective action. We use three different networks (a real Facebook network, an Erdős–Rényi random graph, and a scale-free network) and conduct computational experiments to study contagion dynamics (the size and the speed of diffusion) with respect to the level of homophily. We provide a series of parametric results on the time to achieve a specified contagion spread, on the spread of contagion at different times, and the probability of cascades. We demonstrate that these behaviors are highly nonlinear and nonmonotonic in homophily. Networks with randomly assigned thresholds result in both smaller and slower diffusion compared to the networks characterized by homophily and heterophily.
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Notes
Two disjoint sets of nodes such that nodes within the same set are not connected; but are connected to all nodes in the other set. Consider two sets of nodes; M and L, and let m and l denote the sizes of these sets, respectively. A complete bipartite graph, \(K_{m,l}\), is a bipartite graph that has each vertex from one set of nodes, say M, adjacent to each vertex in the other set, L. For example, \(m=1, l>1\) corresponds to a star, and \(m=2,l=2\) is a square graph.
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This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-17-1-0378. Any opinions, finding, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. Air Force.
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A preliminary version of the paper appeared in the Proceedings of 2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (Korkmaz et al. 2018).
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Korkmaz, G., Kuhlman, C.J., Goldstein, J. et al. A computational study of homophily and diffusion of common knowledge on social networks based on a model of Facebook. Soc. Netw. Anal. Min. 10, 5 (2020). https://doi.org/10.1007/s13278-019-0615-5
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DOI: https://doi.org/10.1007/s13278-019-0615-5