Influence of Couple Patterns on Entropy in Multilayer Networks

摘要

Many real-world systems are networks coupled with other networks, and research on these multilayer networks about their structure properties and functions recently produced significant and remarkable findings. There is one type of multilayer network in which an individual has more than one counterpart on other layer network. For instance, important station on an infrastructure network usually has more than one supporter on its counterpart network for optional access or risk diversification. In this paper, we investigate the influence of couple patterns on information entropy and energy of two layer coupled networks with community structures. Couple patterns refer to the allocation of counterpart numbers according to nodes' degrees and the establishment of interconnections between nodes on different layer networks according to their degree of assortativity. Nodes' degrees and counterpart numbers are assorted based on the tendency of large degree nodes with more counterparts or the reverse. Additional, a pair of nodes on different layer networks can be interconnected according to their degree of assortativity. Under the scenario of a heterogeneous distribution of counterpart numbers, we have found that the influences of couple patterns on entropy and energy are negative. That is, entropy and energy of the two layer coupled network decrease when counterpart number assortativity and/or degree assortativity positively increase, while increase when the two assortativity are negatively enhanced. Moreover, networks with weak community structures extend these influences compared to networks with obvious community structures.