Application of varentropy as a measure of probabilistic uncertainty for complex networks  

作　　者：JIANG Jian WANG Ru PEZERIL Michel WANG Qiuping Alexandre 

机构地区：[1]Institut Superieur des Materiaux et Mecaniques Avarices 44, Avenue F.A. Bartholdi, 72000 Le Mans, France [2]Complexity Science Center, Institute of Particle Physics, Central China Normal University, Wuhan 430079, China [3]LPEC, Faculte des Sciences et Techniques, Universite du Maine, Ave. O. Messiaen, 72035 Le Mans, France [4]College of Information Science and Engineering, Huaqiao University, Quanzhou 362021, China

出　　处：《Chinese Science Bulletin》2011年第34期3677-3682,共6页

基　　金：supported by the Chinese Ministry of Education (2008677010);the National Natural Science Foundation of China (10647125, 10635020, 10975057, 10975062);the Programme of Introducing Talents of Discipline to Universities (B08033)

摘　　要：Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relationship between the varentropy of the scale free distribution and the exponent of power laws as well as network size, we get the optimal design of a scale-free network against random failures. The behaviors of varentropy and the Shannon entropy of double Pareto law degree distribution are analyzed to compare their usefulness. Our conclusion is that varentropy is suitable and reliable.Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relationship between the varentropy of the scale free distribution and the exponent of power laws as well as network size, we get the optimal design of a scale-free network against random failures. The behaviors of varentropy and the Shannon entropy of double Pareto law degree distribution are analyzed to compare their usefulness. Our conclusion is that varentropy is suitable and reliable.

关 键 词：概率不确定性 网络应用 Shannon熵 无标度网络 第二定律 平衡系统 幂律指数 网络规模 

分 类 号：O157.5[理学—数学]