Heterogeneous node copying from hidden network structure

Abstract

Node copying is an important mechanism for network formation, yet most models assume uniform copying rules. Motivated by observations of heterogeneous triadic closure in real networks, we introduce the concept of a hidden network model - a generative two-layer model in which an observed network evolves according to the structure of an underlying hidden layer - and apply the framework to a model of heterogeneous copying. Framed in a social context, these two layers represent a node's inner social circle, and wider social circle, such that the model can bias copying probabilities towards, or against, a node's inner circle of friends. Comparing the case of extreme inner circle bias to an equivalent model with uniform copying, we find that heterogeneous copying suppresses the power-law degree distributions commonly seen in copying models, and results in networks with much higher clustering than even the most optimum scenario for uniform copying. Similarly large clustering values are found in real collaboration networks, lending empirical support to the mechanism.