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arXiv 1906.09082physics.soc-phcs.SI
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双曲空间中的社团检测

Community Detection in the Hyperbolic Space

Matteo Bruno, Sandro Ferreira Sousa, Furkan Gursoy, Matteo Serafino, Francesca V. Vianello, Ana Vranić, Marián Boguñá

摘要:

在双曲空间中嵌入网络可以揭示网络结构的有趣特征,特别是在自相似特征方面。隐度量空间可以被认为是网络的底层结构,它能够保留一些在现实世界网络中通常观察到的有趣特征,例如度分布的异质性,高聚类系数和小世界效应。此外,双曲线平面上的节点的角分布揭示了嵌入式网络的社区结构。值得注意的是,虽然大量的文献比较了知名的社区检测算法,但对于什么定义网络上的理想社区分区仍然没有达成共识。此外,发现在双曲空间中嵌入的网络上的社区的算法已在这里首次进行了研究。我们将嵌入式网络上找到的分区与嵌入步骤之前获得的分区进行比较,无论是合成网络还是两个真实网络。本文的第二部分介绍了我们的管道在意大利选举的背景下的网络转发的应用。我们的研究结果揭示了一个社区结构反映的政治光谱,鼓励进一步研究社区检测算法的应用映射到双曲平面图。

英文摘要:

Embedding a network in hyperbolic space can reveal interesting features for the network structure, especially in terms of self-similar characteristics. The hidden metric space, which can be thought of as the underlying structure of the network, is able to preserve some interesting features generally observed in real-world networks such as heterogeneity in the degree distribution, high clustering coefficient, and small-world effect. Moreover, the angular distribution of the nodes in the hyperbolic plane reveals a community structure of the embedded network. It is worth noting that, while a large body of literature compares well-known community detection algorithms, there is still no consensus on what defines an ideal community partition on a network. Moreover, heuristics for communities found on networks embedded in the hyperbolic space have been investigated here for the first time. We compare the partitions found on embedded networks to the partitions obtained before the embedding step, both for a synthetic network and for two real-world networks. The second part of this paper presents the application of our pipeline to a network of retweets in the context of the Italian elections. Our results uncover a community structure reflective of the political spectrum, encouraging further research on the application of community detection heuristics to graphs mapped onto hyperbolic planes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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