Abstract
We study the properties of the potential overlap between two networks sharing the same set of nodes (a two-layer network) whose respective degree distributions are given. Defining the overlap coefficient as the Jaccard index, we prove that is very close to 0 when and are random and independently generated. We derive an upper bound for the maximum overlap coefficient permitted in terms of , and . Then we present an algorithm based on cross rewiring of links to obtain a two-layer network with any prescribed inside the range . A refined version of the algorithm allows us to minimize the cross-layer correlations that unavoidably appear for values of beyond a critical overlap . Finally, we present a very simple example of a susceptible-infectious-recovered epidemic model with information dissemination and use the algorithms to determine the impact of the overlap on the final outbreak size predicted by the model.
- Received 29 November 2017
DOI:https://doi.org/10.1103/PhysRevE.97.032303
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