A New Framework for Centrality Measures in Multiplex Networks

ABSTRACT Any kind of transportation system, from trains, to buses and ƒights, can be modeled as networks. In biology, networks capture the complex interplay between phenotypes and genotypes. More recently, people and organizations heavily interact with one another using several media (e.g. social media platforms, e-Mail, instant text and voice messages), giving rise to correlated communication networks. Œe non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. Œe problem is even more dicult when the information is distributed across networks (e.g., communication networks in di‚erent media); in this case, it becomes impossible to have a complete, or even partial picture, if situations are analyzed separately within each network due to sparsity. A multiplex network is well-suited to model the complexity of this kind of systems by preserving the semantics associated with each network. Centrality measures are fundamental for the identi€cation of key players, but existing approaches are typically designed to capture a prede€ned aspect of the system, ignoring or merging the semantics of the individual layers. To overcome the aforementioned limitations, we present a Framework for Tailoring Centrality Measures in Multiplex networks (TaCMM), which o‚ers a ƒexible methodology that encompasses and generalizes previous approaches. Œe strength of TaCMM is to enable the encoding of speci€c dependencies between the subnets of multiplex networks to de€ne semantic-aware centrality measures. We develop a theoretically sound iterative method, based on Perron-Frobenius theory, designed to be e‚ective also in highsparsity conditions. We formally and experimentally prove its convergence for ranking computation. We provide a thorough investigation of our methodology against existing techniques using di‚erent types of subnets in multiplex networks. Œe results clearly show the power and ƒexibility of the proposed framework.