论文标题
标记图枚举的递归公式
Recursive Formula for Labeled Graph Enumeration
论文作者
论文摘要
该手稿提出了一个一般递归公式，以估计与代数图相关的纤维的大小，从图表到社交网络分析的重要性汇总统计数据，例如边缘数量（图密度），程度序列，程度分布，结节协变量和程度混合。也就是说，公式估算给出网络属性值的标记图的数量。所提出的方法可以扩展到其他网络属性（例如聚类）以及两部分网络的属性。对于存在替代公式的特殊设置，模拟研究证明了所提出的方法的有效性。我们说明了估计与Barabási-Albert模型相关的纤维大小的方法，该模型是学位分布和程度混合的特性。此外，我们演示了如何使用该方法来评估纤维内图的多样性。
This manuscript presents a general recursive formula to estimate the size of fibers associated with algebraic maps from graphs to summary statistics of importance for social network analysis, such as number of edges (graph density), degree sequence, degree distribution, mixing by nodal covariates, and degree mixing. That is, the formula estimates the number of labeled graphs that have given values for network properties. The proposed approach can be extended to additional network properties (e.g., clustering) as well as properties of bipartite networks. For special settings in which alternative formulas exist, simulation studies demonstrate the validity of the proposed approach. We illustrate the approach for estimating the size of fibers associated with the Barabási--Albert model for the properties of degree distribution and degree mixing. In addition, we demonstrate how the approach can be used to assess the diversity of graphs within a fiber.
