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。%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.
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