Construction and Characteristic Analysis of Two-Layer Complex Network Model

To characterize the homogeneity and heterogeneity between nodes or connecting edges, we considered the multi-relationship attributes of nodes and constructed six dual-layer network models. Firstly, based on node homogeneity, we constructed three homogeneous two-layer network models (GEE,R), (GWW,R) and (GBB,R) using the same generation algorithm for intra-layer connections and random connections for inter-layer connections. Secondly, based on node heterogeneity, we constructed three heterogeneous two-layer network models (GEW,R), (GBE,R) and (GBW,R) using different generation algorithms for intra-layer connections and random connections for inter-layer connections. Then, we derived the average degree analytical expressions and node degree distribution analytical expressions for the six two-layer networks. Finally, according to the differences in inter-layer connection probabilities, we depict the experiments with node degree distribution. Experiments have shown that the node degree distribution of (GEW,R) networks exhibits a bimodal characteristic, while the node degree distribution of (GBE,R) networks presents both Power-law and unimodal mixed characteristics. Overall, this study provides insights into the characteristics of different two-level network models and their application in modeling complex systems.