Coherence Of Complex Networks With Hub Nodes

Network coherence of complex networks with noise is a new research topic,which describes the robustness of consensus dynamics to external noise.In the context of the given problem,the network coherence can be quantified by the Laplacian spectrum of the network.The research focuses on the relationship between the network coherence and the network topology.Since the Laplacian spectrum of a network is determined by the network structure,it is a great challenge to obtain the exact result of the network coherence characterized by the reciprocal sum of all non-zero eigenvalues.The current works on coherence focus on the relationship between coherence and network parameters,and do not study the influence of distance between Hub nodes.In this dissertation,some deterministic networks with Hub nodes are selected as network models,and the effect of distance of Hub nodes on coherence is studied.Based on the regular topology of networks,the analytical expression of network coherence regarding network parameters and distance is obtained,and the relationship between distance between Hub nodes and network coherence is further discussed.The influence of a weight factor and adjacent Hub nodes on coherence is analyzed.Finally,the coherence of weighted tree network and ring tree network is compared.The detailed works are as follows:1.The relationship between distance between Hub nodes and network coherence is discussed.Three kinds of tree network models with Hub nodes are proposed.Based on the regular topology,the analytical expressions of coherence with respect to the distance of Hub nodes and the network size are obtained.The results show that the smaller the distance between Hub nodes and the greater the degree difference,the better the network coherence.In addition,the network coherence increases linearly with the average path length.2.The effect of a weight factor on network coherence is analyzed.Three weight methods are applied to a family of tree networks containing Hub nodes.The exact solution of network coherence about weight factors is obtained.The influence of a weight factor and different weight distributions on network coherence is studied.The results have shown that large weight factor leads to good network coherence.The weight factor has weaker effect on network coherence than the distance between Hub nodes.3.The influence of adjacent Hub nodes on network coherence is studied.A weighted ring tree network with Hub nodes is selected as the research object,and the positions of two Hub nodes are adjusted to make them adjacent and non-adjacent.The analytic expressions of network coherence about weight factor and network parameters are calculated accurately.The results show that adjacent Hub nodes leads to the optimal network coherence,and the coherence of weighted ring tree network is better than that of tree network.