Controllability and Optimization of Complex Networks Based on Bridges

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.

Age-related changes in network controllability are mitigated by redundancy in large-scale brain networks

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Controllability of Flow‐Conservation Transportation Networks with Fractional‐Order Dynamics

“…e direction of the link can represent who is the upstream of the vehicle flow in two nodes. Figure (4) shows the eigenvalue and its maximum geometric multiplicity of case test 1 and substitutes it into the matrix for simplification to obtain column canonical form. And Figures 5 and 6 show the classic OD network and its controller result diagram.…”

“…A complex dynamical network is said to be controllable, if any other state can be reached from its current state through a given control action. e research of controllability of integer-order complex networks has been a hot topic [1][2][3][4][5]. From a transportation networks' perspective, for example, whether the congestion can be eased via the first-best pricing controller on the links is actually a controllability problem.…”

Robustness of Network Controllability with Respect to Node Removals Based on In-Degree and Out-Degree

“…For example, degree-based attacks have been found to be more harmful to network controllability than random attacks [ 10 ], while betweenness-based attacks are more damaging in most real-world networks [ 11 ]. Additionally, attacking bridge links, which results in a disconnected network, has been shown to be an effective way to destroy network controllability [ 12 ]. Another approach to targeted attack strategies involves identifying critical nodes and links whose removal increases the number of driver nodes [ 6 ].…”