Inter-layer Degree Correlations in Heterogeneously Growing Multiplex Networks

TL;DR

This paper investigates inter-layer degree correlations in heterogeneously growing multiplex networks, revealing new analytical results and surprising correlations even in random growth scenarios, supported by simulations.

Contribution

It provides the first analytical characterization of inter-layer degree distributions and correlations in heterogeneously growing multiplex networks, including both preferential and uniform growth models.

Findings

Non-trivial inter-layer degree correlations emerge in steady state.

Inter-layer correlations occur even in random growth scenarios.

The average degree relation for nodes with degree k in one layer is identical across growth schemes.

Abstract

The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first analyze the case of two preferentially growing layers and find a closed-form expression for the inter-layer degree distribution, and demonstrate that non-trivial inter-layer degree correlations emerge in the steady state. Then we focus on the case of uniform growth. Surprisingly, inter-layer correlations arise in the random case, too. Also, we observe that the expression for the average layer-2 degree of nodes whose layer-1 degree is k, is identical for the uniform and preferential schemes. Throughout, theoretical predictions are corroborated using Monte Carlo simulations.