极小Cayley图的确定性小世界网络模型

小世界网络的确定性模型研究是复杂网络建模领域的重要分支,通过分析Cayley图的极小性与小世界特性的关联,提出一种基于极小Cayley图构造小世界网络的确定性模型．模型通过选择满足条件的极小Cayley图,恰当地扩展其生成集,构造出一类对称性强且结构规则的小世界网络．结果表明, 和现有模型不同,该模型可根据需求构造常数度或非常数度网络,且生成网络不仅具有较高的聚集系数和低的网络直径,而且是节点对称的,在通信网络、结构化P2P覆盖网络等实际领域的拓扑结构设计中具有重要应用．

Deterministic small-world network model based on minimal Cayley graph

The research on deterministic small-world network model is an important branch of complex network modeling. This paper analyzes the small-world property of the minimal Cayley graph and proposes a deterministic small-world network model based on minimal Cayley graph. The model constructs a class of small-world networks with high symmetry by selecting a minimal Cayley graph, and appropriately expands its generating set. Compared with the existing models, this model can be used flexibly to get small-world networks with const degree or variable degree, which is adaptable for the disign and analysis of the real networks such as communication network and P2P overlay network.