Heterogeneous node copying from hidden network structure

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. Node duplication is an established model of network formation, whereby an existing node is duplicated, and edges are formed with uniform probability to the neighbours of the duplicated node. Here, the author proposes a copying model where links are copied depending on hidden interactions between nodes, and shows analytically and numerically that this leads to higher network clustering than in the uniform copying case, a property that is also found in real collaboration networks.