多阶邻接分布熵下的复杂网络节点相似性分析方法

Analysis method of nodes similarity with multi-layer adjacency entropy

为弥补宏观网络结构熵描述整体结构信息却忽略局部,而微观熵描述节点信息又较浅层单一的不足,提出一种节点多阶邻接分布熵,以度量节点多阶邻居的分布特征信息,便于在自定义阶数尺度上分析复杂网络结构.该熵随多阶邻居阶数的增长而增大,并在节点的离心率处收敛.在给定的尺度下,节点各阶邻居分布越均匀则多阶邻接熵越大.基于多阶邻接分布相对熵,比较节点间多阶邻居分布的差异,从而以一种新的视角分析节点相似性,并与其他有代表性的节点相似性方法进行了实验对比,在互相似比和传播能力指标上,取得了更好的结果.

Network structure macroscopic entropy attaches great importance to whole structure but takes little notice of local information,and network structure microscopic entropy superficially describes node information with single layer or path.The multi-layer adjacency entropy is proposed to measure the distribution characteristics of nodes’multi-layer neighbors in this paper,which has a positive effect on the research of complex network structure on the optional layer scale.The entropy will increase with the increase of the layer scale of multi-layer neighbors and converges at the eccentricity of the node.On a given scale,the more even distribution of the node multi-layer neighbors are,the higher the multi-layer adjacency entropy is.Based on the multi-layer adjacency relative entropy,by comparing multi-layer neighbors distribution among nodes,the similarity of nodes is analyzed from a new perspective.Compared with other representative methods of nodes similarity,the multi-layer adjacency relative entropy got better result on the index of mutual similarity ratio and transmission ability.