Growing Multiplex Networks with Arbitrary Number of Layers

Abstract

This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the special case of homogeneous growth, and are limited to the state state (that is, the limit of infinite size). In the present paper, we obtain closed-form solutions for the joint degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state. Heterogeneous growth means that each incoming node establishes different numbers of links in different layers. We consider both uniform and preferential growth. We then extend the analysis of the uniform growth mechanism to arbitrary times. We obtain a closed-form solution for the time-dependent joint degree distribution of a growing multiplex network with arbitrary initial conditions. Throughout, theoretical findings are corroborated with Monte Carlo simulations. The results shed light on the effects of the initial network on the transient dynamics of growing multiplex networks, and takes a step towards characterizing the temporal variations of the connectivity of growing multiplex networks, as well as predicting their future structural properties.

References in corpus (14)

• The structure and dynamics of multilayer networks
• Diffusion dynamics on multiplex networks
• Multirelational Organization of Large-scale Social Networks in an Online World
• Evolutionary games on multilayer networks: A colloquium
• Emergence of network features from multiplexity
• Competing spreading processes on multiplex networks: awareness and epidemics
• Measuring and modelling correlations in multiplex networks
• Weighted Multiplex Networks
• Weak percolation on multiplex networks
• Non-linear growth and condensation in multiplex networks
• Routes to thermodynamic limit on scale-free networks
• Strategical incoherence regulates cooperation in social dilemmas on multiplex networks
• Supersymmetric multiplex networks described by coupled Bose and Fermi statistics
• Transition from small to large world in growing networks

Cited by in corpus (4)

• Measuring and modelling correlations in multiplex networks
• The new challenges of multiplex networks: measures and models
• Big Data Processing in Complex Hierarchical Network Systems
• Flow approaches to community detection in complex network systems