论文标题
在双曲线空间中建模网络社区时，维度很重要
Dimension matters when modeling network communities in hyperbolic spaces
论文作者
论文摘要
在过去的十年中，事实证明，随机双曲线图在提供现实世界网络的许多关键特性的几何解释方面已被证明，包括强聚类，高可通道性和异构度分布。这些特性在与互联网，运输，大脑或流行病网络一样多样的系统中无处不在，因此在恒定负曲率表面上的双曲网络解释中统一了这些特性。尽管一些研究表明，双曲线模型可以生成社区结构，但在实际网络中观察到的另一个显着特征，我们认为当前模型正在忽略选择潜在空间维度的选择，以充分代表聚类的网络数据。我们表明，在节点之间的相似性限制连接概率的相似性方面，最低维模型与其较高维度对应物之间存在重要的定性差异。由于更多的维度还增加了代表社区的角群的最近邻居的数量，因此只有一个维度可以使我们产生更现实和多样化的社区结构。
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree distributions. These properties are ubiquitous in systems as varied as the internet, transportation, brain or epidemic networks, which are thus unified under the hyperbolic network interpretation on a surface of constant negative curvature. Although a few studies have shown that hyperbolic models can generate community structures, another salient feature observed in real networks, we argue that the current models are overlooking the choice of the latent space dimensionality that is required to adequately represent clustered networked data. We show that there is an important qualitative difference between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities. Since more dimensions also increase the number of nearest neighbors for angular clusters representing communities, considering only one more dimension allows us to generate more realistic and diverse community structures.
