Research On Robustness Of Complex Networks Based On Hyperbolic Space

With the development of the economy,society has rapidly entered the era of network,people have put forward higher requirements on the reliability and security of networks closely related to national economy and people's livelihood.The theoretical significance and application value of the research on navigability and robustness of complex networks are increasingly prominent.The research on the robustness of complex networks analyzes the network's ability to resist node failure or malicious attacks from the perspective of the network topology,measures the importance of network nodes and edges,and provides guidance for network structure optimization and robustness improvement.The hyperbolic geometric framework can provide a new research perspective for the research of robustness of complex networks.In the hyperbolic space,the nodes in the network are given hyperbolic coordinates,and the hyperbolic space implied by complex networks has become a powerful method for studying network topology.To embed a complex network into its hidden hyperbolic space,the accuracy of the hyperbolic mapping algorithm is crucial.To solve the problem that the time complexity of the existing hyperbolic mapping algorithm is too high to be applied to large networks,this paper proposes a fast hyperbolic mapping algorithm HCHSM,which is based on the network evolution model,the community sector model in the hyperbolic space and the hierarchical community structure of complex networks.First,an index CS for measuring the similarity of the community is proposed.Then,based on the network's hierarchical community structure and community sector model,a hierarchical community ranking algorithm based on the CS index is proposed to determine the community's order on the hyperbolic disc.The network is mapped into the hyperbolic space according to the order and angle range of corresponding sectors of the second-level community.Compared with the existing hyperbolic mapping algorithm,HCHSM reduces the time complexity to linearity in large sparse networks while ensuring good mapping accuracy.Not only that,the network embedding hyperbolic space using HHCSM algorithm also has good navigability.In order to study the robustness of different real networks under various attack strategies,first,using the hyperbolic coordinates of the network nodes in the hyperbolic space and the navigability of the network after embedding the hyperbolic space,two importance indicators for describing the nodes are proposed,which are based on the centrality of the first-order neighborhood hyperbolic coordinates of the nodes index HNC and central index HISC based on global information of hyperbolic space.Then based on the community structure of the network,the CSC,an important node indicator that measures good internal and external connections in the community,is depicted,and an attack strategy ACSC based on the community structure is proposed.Based on community structure of the network,combined with the node importance indicators HNC and HISC,the local attack strategies BHNC and BHISC for the bridge nodes are proposed.Experimental results show that the greater the HNC or HISC value of a node,the greater its impact on the robustness of the network,community attack strategies based on CSC indicators are no less than community attacks based on degree centrality and betweenness centrality,local attack strategies BHNC and BHISC have the same attack effect in the network,and both can decompose the network faster,calculated attacks have a great impact on the network efficiency and maximum connected subgraph size.