基于解释结构模型的复杂网络节点重要性计算

Importance calculation of complex network nodes based on interpretive structural modeling method

针对有向复杂网络节点重要性评估问题,提出基于解释结构模型的节点重要性度量方法.应用解释结构模型,将有向网络节点间关系矩阵化,获得相应的邻接矩阵和可达矩阵;对可达矩阵进行区位、级位划分;对矩阵进行缩减、删除越级与自身相连关系;得到网络的递阶有向图.对网络矩阵进行赋权模拟演化,给出网络区域重要性与级位重要性辨识划分.将该方法应用于ARPA有向网络、有向随机网络和有向无标度网络中,与其他4种网络节点排序方法进行比较.结果表明,该方法不仅适用于有向网络层级划分与辨识,而且适用于有向网络的节点排序计算.

A node importance measurement method based on interpretive structural model was proposed in order to solve the problem of evaluating the importance of nodes in a directed complex network.The relationship between nodes in the directed network was matrixes,and the corresponding adjacency matrix and reachability matrix were obtained by applying the interpretative structural model.Then the location and rank of the reachable matrix were partitions.The matrix was reduced,and the relationship between leapfrog and itself was deleted.The hierarchical directed graph of the network was obtained.The network matrix was empowered to simulate evolution,and the importance of network area and identification of rank importance were given.The method was applied to ARPA directed networks,directed random networks and directed scale-free networks,and compared with other four network node ranking methods.Results show that the method is applicable not only to the hierarchical division and identification of directed networks,but also to the sorting of nodes in directed networks.