Communication in Multiplex Transportation Networks
Silvia Noschese, Lothar Reichel
TL;DR
The paper tackles how to quantify and enhance communication in multiplex transportation networks by developing two complementary frameworks: efficiency via a multiplex path-length formulation and popularity via multiplex total communicability. It introduces concrete constructions such as the multiplex 1-path length matrix $P^1$, the multiplex $K$-path length matrix $P^K$ using min-plus algebra, and the corresponding efficiency measures $e_{\mathcal{A}}^K(\gamma)$, along with a structured Perron-sensitivity analysis to identify edge-strengthening opportunities. A parallel popularity-based approach centers on $tc_B(\gamma)$ and its Perron-based approximation $Pc_B(\gamma)$, with robust bounds and a methodology to select influential intra-layer edges through the structured perturbation of block-diagonal components. Numerical tests on Air500, Autobahn, European airlines, and London transport networks illustrate how the two approaches yield complementary guidance for infrastructure planning, enabling scalable analysis via Perron-based surrogates when exact matrix functions are intractable. The work provides actionable, mathematically grounded strategies for improving multiplex connectivity in transportation systems while offering scalable tools for large-scale networks.
Abstract
Complex networks are made up of vertices and edges. The edges, which may be directed or undirected, are equipped with positive weights. Modeling complex systems that consist of different types of objects leads to multilayer networks, in which vertices in distinct layers represent different kinds of objects. Multiplex networks are special vertex-aligned multilayer networks, in which vertices in distinct layers are identified with each other and inter-layer edges connect each vertex with its copy in other layers and have a fixed weight $γ>0$ associated with the ease of communication between layers. This paper discusses two different approaches to analyze communication in a multiplex. One approach focuses on the multiplex global efficiency by using the multiplex path length matrix, the other approach considers the multiplex total communicability. The sensitivity of both the multiplex global efficiency and the multiplex total communicability to structural perturbations in the network is investigated to help to identify intra-layer edges that should be strengthened to enhance communicability.