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Counting five-node subgraphs
arXiv - CS - Discrete Mathematics Pub Date : 2020-09-23 , DOI: arxiv-2009.11318
Steve Lawford

We propose exact count formulae for the 21 topologically distinct non-induced connected subgraphs on five nodes, in simple, unweighted and undirected graphs. We prove the main result using short and purely combinatorial arguments that can be adapted to derive count formulae for larger subgraphs. To illustrate, we give analytic results for some regular graphs, and present a short empirical application on real-world network data. We also discuss the well-known result that induced subgraph counts follow as linear combinations of non-induced counts.

中文翻译:

计数五节点子图

我们为五个节点上的 21 个拓扑不同的非诱导连通子图提出了精确计数公式,这些子图在简单、未加权和无向图中。我们使用简短且纯组合的参数证明了主要结果,这些参数可适用于推导出较大子图的计数公式。为了说明这一点,我们给出了一些规则图的分析结果,并在现实世界的网络数据上给出了一个简短的经验应用。我们还讨论了众所周知的结果,诱导子图计数遵循非诱导计数的线性组合。
更新日期:2020-09-25
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