Abstract
Most real-world networks have a modular structure, i.e., they are composed of clusters of well connected nodes, with relatively lower density of links across different clusters. Here we report on our studies of a simple cascading process in a structured heterogeneous population composed of two loosely coupled communities. We demonstrate that under certain conditions the cascading dynamics in such a network has a two-tiered structure that characterizes activity spreading at different rates in the communities. We also demonstrate that the structure has implication on problems such as influence maximization. In particular, it is shown that targeting heuristics that work provably well for homogenous networks can produce significantly sub-optimal results for heterogenous networks. We suggest a simple modification of the heuristics that accounts for the community structure, and observe improved performance.
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Notes
- 1.
Furthermore, we would like to argue that the modified model with integer threshold also seems more plausible from the social-choice standpoint. Indeed, it is hard to imagine that, when trying to make a decision based on our friends’ recommendations, we normalize the number of recommendations by the total number of our friends.
- 2.
Θ(x) = 1 if x ≥ 0, and Θ(x) = 0 otherwise.
- 3.
Strictly speaking, P(k; t) is given by a binomial distribution B(N 0, p). However, in the limit of large network sizes considered here, we approximate the binomial distribution by the Poisson distribution as it simplifies the analysis.
- 4.
Due to space restrictions, here we report our findings only for the integer threshold model on synthetic graphs.
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Galstyan, A. (2013). Activation Cascades in Structured Populations. In: Michelucci, P. (eds) Handbook of Human Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8806-4_63
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DOI: https://doi.org/10.1007/978-1-4614-8806-4_63
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