复杂网络的冯诺依曼熵  

The Von Neumann Entropy of Complex Networks

作　　者：袁炜罡[1] 张晓东[1] Yuan Weigang Zhang Xiaodong(Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, Chin)

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《宁夏大学学报（自然科学版）》2016年第3期288-293,共6页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271256);上海市教委科研创新项目资助(14ZZ016);高等学校博士学科点专项科研基金资助项目(20130073110075)

摘　　要：主要研究了复杂网络的冯诺依曼熵.结论表明,一般情况下,冯诺依曼熵不随边的增加而严格单调增加.其次,定义了星生成图和路生成图,并给出了熵与这两类图的联系.最后,利用3种经典随机图模型和随机树模型,证明了平均场意义下冯诺依曼熵随复杂网络的边数和直径递增.The von Neumann entropy of network is studied.The result shows that von Neumann entropies do not increase as edges increase.Star-generate graph and path-generate graph are defined and the relationship of entropy and these two series of graphs are given.By mean-field theorem（MFT）,von Neumann entropies increase as edges and diameters of networks increase.

关 键 词：冯诺依曼熵 随机图 平均场 

分 类 号：O157.6[理学—数学]