Abstract
In a complex network, each edge has different functions on controllability of the whole network. A network may be out of control due to failure or attack of some specific edges. Bridges are a kind of key edges whose removal will disconnect a network and increase connected components. Here, we investigate the effects of removing bridges on controllability of network. Various strategies, including random deletion of edges, deletion based on betweenness centrality, and deletion based on degree of source or target nodes, are used to compare with the effect of removing bridges. It is found that the removing bridges strategy is more efficient on reducing controllability than the other strategies of removing edges for ER networks and scale-free networks. In addition, we also found the controllability robustness under edge attack is related to the average degree of complex networks. Therefore, we propose two optimization strategies based on bridges to improve the controllability robustness of complex networks against attacks. The effectiveness of the proposed strategies is demonstrated by simulation results of some model networks. These results are helpful for people to understand and control spreading processes of epidemic across different paths.
Highlights
Many natural and manmade systems can be modeled as complex networks which consist of nodes and edges
Electric power networks can be regarded as complex networks formed by a large number of substations connected by transmission lines; citation networks can be regarded as complex networks composed by a large number of scholars contact through mutual citation of articles; in addition, biochemical networks, food webs, social networks, etc. all exist in form of complex networks. e basic research of complex networks is to understand the static structure and dynamic characteristics of networks [1], such as the construction of networks, the topological characteristics of networks, the community structure [2], and synchronization of networks [3, 4]
We investigate the controllability of complex networks when bridges are iteratively deleted by attacks
Summary
Many natural and manmade systems can be modeled as complex networks which consist of nodes and edges. Complex network failures caused by attacking or corrupting certain edges and nodes would lead networks out of control. Chen et al [10] studied the impact on controllability when nodes of Complexity networks were attacked. Eir research studies demonstrate that random failures have little effect on controllability, while attacking nodes based on degree, attacking edges based on betweenness, and attacking the longest simple paths are intensely effective on controllability [13]. Xiao et al [18] proposed a dynamic optimization method to improve the robustness of arbitrary structural networks against target attacks, and the method only exchanges edges but does not change the nodes’ degree. En, we propose two optimization strategies based on bridges to improve controllability robustness of complex networks against attacks Little attention has been paid to the importance of bridges on controllability of complex networks. erefore, we investigated the effects of removing bridges on controllability of network. en, we propose two optimization strategies based on bridges to improve controllability robustness of complex networks against attacks
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