基于模体的复杂网络测度量研究

The measurement of complex network based on motif

针对复杂网络拓扑结构中模体的存在性,在传统的顶点度和边聚类系数定义的基础上,提出了基于模体的顶点度和边度来衡量网络中顶点和边的重要性.用Rand-ESU算法对不同规模的8个网络进行模体检测,验证了网络中模体的存在性,重点分析了Karate网络和Dolphin网络中模体的结构和特征.用Pearson相关系数衡量基于模体的顶点度与传统顶点度、基于模体的边度与边聚类系数的相关性,仿真分析结果表明相关性大小与模体种类有关,基于模体的顶点度和边度是对原定义的一种改进和拓展,更全面地刻画了顶点和边在网络中的重要性.

According to the existence of motif in complex network topology structure, the motif-based node degree and edge degree are proposed to measure the importance of node and edge in the network on the basis of the traditional node degree and edge clustering coefficient. The Rand-ESU algorithm is used for motif detection of eight different scale networks, and the result demonstrates the existence of motif. The Rand-ESU algorithm is also used for analyzing the motif structures and characteristics in Karate network and Dolphin network. The Pearson correlation coefficient is used to measure the correlations of motif-based node degree and traditional node degree, motif-based edge degree and edge clustering coefficient. The results of simulation analysis show that the correlations are related to the motif species. The definitions of motif-based node degree and edge degree are the improvement and development of original definitions, and they comprehensively depict the importance of node and edge in the network.