论文标题
具有社区结构的ABCD随机图模型的模块化
Modularity of the ABCD Random Graph Model with Community Structure
论文作者
论文摘要
社区检测的人工基准（ABCD）图是一个随机图模型，具有社区结构和幂律分布的学位和社区规模。该模型生成具有与众所周知LFR ONE相似的属性的图形，并且可以调整其主要参数$ξ$以模仿LFR模型中的对应物，即混合参数$μ$。 在本文中，我们研究了ABCD模型的各种理论渐近特性。特别是，我们分析了模块化函数，可以说是社区检测背景下网络最重要的图形属性。实际上，模块化函数通常用于测量网络中社区结构的存在。它在许多社区检测算法中也被用作质量功能，包括广泛使用的Louvain算法。
The Artificial Benchmark for Community Detection (ABCD) graph is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known LFR one, and its main parameter $ξ$ can be tuned to mimic its counterpart in the LFR model, the mixing parameter $μ$. In this paper, we investigate various theoretical asymptotic properties of the ABCD model. In particular, we analyze the modularity function, arguably, the most important graph property of networks in the context of community detection. Indeed, the modularity function is often used to measure the presence of community structure in networks. It is also used as a quality function in many community detection algorithms, including the widely used Louvain algorithm.
