复杂网络稀疏性的统计物理研究综述

A review on statistical physics for the sparsity of complex networks

大多数实际存在的复杂网络是稀疏的,即网络平均度远小于节点数:k—N.到目前为止,关于这一性质的起源,它对于网络功能与网络上动力学过程的影响,可能的应用价值的研究还都远远不足.实际上,稀疏性与网络的其它拓扑性质密切相关.近几年来,人们对复杂网络稀疏性的相关效应从理论和实验两个方面都做了深入的研究,但是,还缺乏原理性的探讨.从统计物理的视角出发,稀疏性应当被看作复杂系统中个体之间相互作用的涌现性质,而不应当是现有模型中先验的前提.本文拟就复杂网络稀疏性的统计物理研究作一综述.

Most practically existing complex networks are sparsely connected, namely, the average degrees of them are much smaller than their total numbers of nodes： k^- 〈〈N. Up till now, the research on the origin of this property, its effects on functions of networks and dynamic processes on networks,and its possible applications have been still far less than adequate. Actually, sparsity is closely related with other topological properties. In recent years, much progress has been made on sparseness of complex networks from both theoretic and experimental aspects. However, principle conclusion is still anticipated. From the view point of statistical physics, it is believed that the sparsity of networks should be accounted as an emergent property of interactions between individuals in complex systems, instead of e priori prerequisite for existing models. In the present paper, we attempt to review previous investigations with statistical physics on the sparseness of complex networks.