Analysis Of Cut Vertex In The Control Of Complex Network

The research on the control characteristics of complex networks is a hot topic in the researching direction of complex networks in recent years,and the problem of network controllability is also an important goal of complex network research.With the in-depth study of complex networks,people have found that when a network selects appropriate driving nodes so that the network can reach the desired target state,then the network is controllable.In the controllability of complex networks,structure controllability studies the minimum input required when the network is completely controllable,while exact controllability further solves the controllability problem in networks with different structures.However,research in the control of complex networks shows that even though some networks meet the controllability requirements of the network in theory,the cost or time required in the control process is too high,which is not in line with the actual requirements.In view of this phenomenon,the control energy problem of complex network is studied,and the control energy of network can be reduced by adopting a reasonable control method.For the complex networks,the control performance of complex networks is affected by the characteristics of their network structures.As a type of key nodes in the network structure,cut vertexes are essential for network connectivity because their removal will disconnect the network.Despite their fundamental importance,the influence of cut vertexes on network control is still uncertain.Therefore,by studying the cut vertexes,we can find out what effects the cut vertexes have on the network control performance.Here,we reveal the relationship between cut vertexes and driver nodes,and find that driver nodes tend to avoid cut vertexes.In the control energy of the network,driving cut vertexes reduces the energy required for controlling complex networks,since the cut vertexes are located near the middle of the longest control chains.By employing three different node failure strategies,we investigate the impact of cut vertexes failure on the energy required.The results show that cut vertex failures markedly increases the control energy because cut vertexes are larger-degree nodes.Our results deepen the understanding of the structural characteristic in network control.