Enhancing multiplex global efficiency

08/18/2023

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by   Silvia Noschese, et al.

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Modeling complex systems that consist of different types of objects leads to multilayer networks, in which vertices are connected by both inter-layer and intra-layer edges. In this paper, we investigate multiplex networks, in which vertices in different layers are identified with each other, and the only inter-layer edges are those that connect a vertex with its copy in other layers. Let the third-order adjacency tensor 𝒜∈^N× N× L and the parameter γ≥ 0, which is associated with the ease of communication between layers, represent a multiplex network with N vertices and L layers. To measure the ease of communication in a multiplex network, we focus on the average inverse geodesic length, which we refer to as the multiplex global efficiency e_𝒜(γ) by means of the multiplex path length matrix P∈^N× N. This paper generalizes the approach proposed in <cit.> for single-layer networks. We describe an algorithm based on min-plus matrix multiplication to construct P, as well as variants P^K that only take into account multiplex paths made up of at most K intra-layer edges. These matrices are applied to detect redundant edges and to determine non-decreasing lower bounds e_𝒜^K(γ) for e_𝒜(γ), for K=1,2,…,N-2. Finally, the sensitivity of e_𝒜^K(γ) to changes of the entries of the adjacency tensor 𝒜 is investigated to determine edges that should be strengthened to enhance the multiplex global efficiency the most.