Cluster-based topological features of nodes in a multiplex network-from a network of networks perspective

In the gathered multiplex systems, nodes inherit a part of their original system's topological features, as in the world economic system, national policies and resource distribution bring industry advantages and resource advantages to the domestic industry. Although they represent one of the important original topological features of nodes, the inherited topological features of nodes have not received sufficient attention and have hardly been analyzed by existing network models. In our research, we defined the inherited topological features of nodes as 'cluster-based topological features. To accurately calculate the cluster-based topological features of nodes in multiplex networks, we first provide a network model to summarize the multiplex networks into a calculable network of networks (NoN). Based on our network model, we propose a series of algorithms for calculating industries' cluster-based topological features. Our calculating process contains 2 steps: 'abstracting' the NoN into one-layer calculable network; 'inheriting' subnetworks' topological features into the inner nodes. Our network model and calculation algorithms are applied in a series of theoretical and empirical multiplex networks. The results not only confirm the realizability of our model but also produce several interesting findings, the most important of which is that some unremarkable nodes in multiplex network may have a very high contributory value from NoN perspective.