Inter-layer Degree Correlations in Heterogeneously Growing Multiplex Networks

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 in a simple two-layer setting. We first analyze the case of two preferentially growing layers and find a closedform 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. We observe that 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.