【作者】 徐新平； 刘峰；

【Author】 Xinping Xu, Feng Liu ( Institute of Particle Physics, Huazhong Normal University, Wuhan 430079, China) ( Institute of High Energy Physics, Chinese Academy of Science, Beijing 100049, China)

【机构】 华中师范大学粒子物理研究所；

【摘要】 本文研究了微正则系综,正则系综和巨正则系综中网络的统计性质。在度序列固定约束条件下,我们计算了系综中两个节点间的连接几率,发现连接几率与两节点度的乘积成正比。这一结果可以用来解释网络增长模型中的优先连接机制,并为真实网络和网络模型中广泛采用的线性优先连接提供理论依据。另外,我们应用系综方法研究网络中节点的关联性质。最后讨论了复杂网络系综方法的可能应用。更多还原

【Abstract】 The network properties of a micro-canonical ensemble, canonical ensemble and grand canonical ensemble are studied. The connection probability between two nodes is calculated when the ensembles subject to the constraints imposed by the degree sequence. It is found that the connection probability between two nodes is proportional to the product of the degrees. This proportionality can be interpreted as justifying the conventional rule of linear preferential attachment in growing networks and provides theoretical evidence in support of the linear preferential attachment widely exists in real networks and adopted as a crucial assumption in growing network models. The properties of correlations are also studied using the ensemble approach. Finally, possible applications of the ensemble approach in complex network study are discussed.更多还原