论文
arXiv
ComplexNetwork
中文标题
通过三元闭合构建强聚类随机图:度相关性与聚类谱
English Title
Strongly clustered random graphs via triadic closure: Degree correlations and clustering spectrum
Lorenzo Cirigliano, Gareth J. Baxter, Gábor Timár
发布时间
2026/3/5 07:25:09
来源类型
preprint
语言
en
摘要
中文对照

现实世界网络通常表现出强烈的传递性,具有非平凡的局部聚类谱和度相关性。这些特征在可处理的网络模型中难以建模,阻碍了对这类复杂网络结构的理论理解。本文通过一种强聚类随机图模型解决该问题,其中随机骨架中的每个三元组以一定概率被闭合。尽管所得图的局部结构具有复杂的环状特性,我们仍给出了局部聚类谱和度相关性的精确表达式,填补了该随机图模型理论描述的空白。特别地,我们发现高传递性伴随正度相关性,且聚类谱呈现非平凡结构。精确的渐近解析结果得到了大规模数值模拟对有限尺寸效应的详尽表征的补充。

English Original

Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modelled in tractable network models, creating an obstacle to the theoretical understanding of such complex network structures. Here, we address this problem using a model for strongly clustered random graphs in which each triad of a random backbone is closed with a certain probability. Despite the intricate loopy local structure of the graphs obtained, we provide exact expressions for the local clustering spectrum and the degree correlations, filling the gap in the theoretical description of this model for random graphs. In particular, we find positive degree assortativity accompanies high transitivity, and non-trivial structure in the clustering spectrum. Exact asymptotic analytical results are complemented with extensive numerical characterization of finite size effects.

元数据
arXiv2603.04669v1
来源arXiv
类型论文
抽取状态raw
关键词
ComplexNetwork
physics.soc-ph
cond-mat.dis-nn