2018/05/22 by Johann H. Martínez, Stefano Boccaletti, В. В. Макаров +2 · 5 citations
Mathematics · Physics and Astronomy · #Algebraic connectivity #Algebraic number #Artificial intelligence #Combinatorics #Complex Network Analysis Techniques #Computer science #Eigenvalues and eigenvectors #Feature (linguistics) #Image (mathematics) #Laplace operator #Laplacian matrix #Layer (electronics) #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Multiplex #Opinion Dynamics and Social Influence #Physics #Similarity (geometry) #Theoretical and Computational Physics #Theoretical computer science #Topology (electrical circuits) #physics.soc-ph
paper · pdf · doi:10.1016/j.physa.2018.07.008
published in Physica A Statistical Mechanics and its Applications 510, 671-677 (Elsevier BV) · 9 pages, 5 figures
arxiv created 2018/05/22 · openalex created_date 2018/06/01 · openalex publication_date 2018/07/17 · arxiv updated 2018/08/15 · openalex updated_date 2026/08/05
The way the topological structure goes from a decoupled state into a coupled one in multiplex networks has been widely studied by means of analytical and numerical studies, involving models of artificial networks. In general, these experiments assume uniform interconnections between layers offering, on the one hand, an analytical treatment of the structural properties of multiplex networks but, on the other hand, loosing applicability to real networks where heterogeneity of the links' weights is an intrinsic feature. In this paper, we study 2-layer multiplex networks of musicians whose layers correspond to empirical datasets containing, and linking the information of: (i) collaboration between them and (ii) musical similarities. In our model, connections between the collaboration and similarity layers exist, but they are not ubiquitous for all nodes. Specifically, inter-layer links are created (and weighted) based on structural resemblances between the neighborhood of an artist, taking into account the level of interaction at each layer. Next, we evaluate the effect that the heterogeneity of the weights of the inter-layer links has on the structural properties of the whole network, namely the second smallest eigenvalue of the Laplacian matrix (algebraic connectivity). Our results show a transition in the value of the algebraic connectivity that is far from classical theoretical predictions where the weight of the inter-layer links is considered to be homogeneous.