A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level, scientists studie
d interdependent multilayer networks. In this letter, we introduce a new kind of interdependent multilayer networks, i.e., interconnecting networks, for which the component networks are coupled each other by sharing some common nodes. Based on the empirical investigations, we revealed a common feature of such interconnecting networks, namely, the networks with smaller averaged topological differences of the interconnecting nodes tend to share more nodes. A very simple node sharing mechanism is proposed to analytically explain the observed feature of the interconnecting networks.
This manuscript serves as an online supplement of a preprint, which presents a study on a kind of bilayer networks where some nodes (called interconnecting nodes) in two layers merge. A model showing an important general property of the bilayer netwo
rks is proposed. Then the analytic discussion of the model is compared with empirical conclusions. We present all the empirical observations in this online supplement.
We present a model, in which some nodes (called interconnecting nodes) in two networks merge and play the roles in both the networks. The model analytic and simulation discussions show a monotonically increasing dependence of interconnecting node top
ological position difference and a monotonically decreasing dependence of the interconnecting node number on function difference of both networks. The dependence function details do not influence the qualitative relationship. This online manuscript presents the details of the model simulation and analytic discussion, as well as the empirical investigations performed in eight real world bilayer networks. The analytic and simulation results with different dependence function forms show rather good agreement with the empirical conclusions.
