提出混合图论模型，同时捕捉社交网络中的枢纽与密集社区结构。
Graphon Mixtures
- 用图论混合模型生成兼具稀疏与稠密特性的图序列。
- 通过最大度条件识别枢纽，可估计枢纽归一化度及稀疏成分图论。
- 适用于社交网络、引文图等复杂网络分析，适合关注结构建模的研究者。
社交网络通常包含少量大型枢纽节点和大量小型密集社区。本文提出一种生成模型，同时捕捉枢纽和密集结构。基于线图上图论的最新成果，该模型为图论混合模型，可生成由稀疏与稠密图组合而成的图序列。我们提出稀疏图的新条件（最大度），以识别枢纽节点。理论上证明可估计枢纽的归一化度，以及稀疏成分对应的图论。在合成数据、引文图和社交网络上验证方法，展示了显式建模稀疏图的优势。
原文摘要 · Abstract (English)
Social networks have a small number of large hubs, and a large number of small dense communities. We propose a generative model that captures both hub and dense structures. Based on recent results about graphons on line graphs, our model is a graphon mixture, enabling us to generate sequences of graphs where each graph is a combination of sparse and dense graphs. We propose a new condition on sparse graphs (the max-degree), which enables us to identify hubs. We show theoretically that we can estimate the normalized degree of the hubs, as well as estimate the graphon corresponding to sparse components of graph mixtures. We illustrate our approach on synthetic data, citation graphs, and social networks, showing the benefits of explicitly modeling sparse graphs.
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