Kovács Bianka, Balogh Sámuel G, Palla Gergely
Department of Biological Physics, Eötvös Loránd University, Pázmány P. stny. 1/A, 1117, Budapest, Hungary.
MTA-ELTE Statistical and Biological Physics Research Group, Pázmány P. stny. 1/A, 1117, Budapest, Hungary.
Sci Rep. 2022 Jan 19;12(1):968. doi: 10.1038/s41598-021-04379-1.
Hyperbolic network models have gained considerable attention in recent years, mainly due to their capability of explaining many peculiar features of real-world networks. One of the most widely known models of this type is the popularity-similarity optimisation (PSO) model, working in the native disk representation of the two-dimensional hyperbolic space and generating networks with small-world property, scale-free degree distribution, high clustering and strong community structure at the same time. With the motivation of better understanding hyperbolic random graphs, we hereby introduce the dPSO model, a generalisation of the PSO model to any arbitrary integer dimension [Formula: see text]. The analysis of the obtained networks shows that their major structural properties can be affected by the dimension of the underlying hyperbolic space in a non-trivial way. Our extended framework is not only interesting from a theoretical point of view but can also serve as a starting point for the generalisation of already existing two-dimensional hyperbolic embedding techniques.
近年来，双曲网络模型受到了广泛关注，主要是因为它们能够解释现实世界网络的许多独特特征。这类模型中最广为人知的之一是流行度-相似度优化（PSO）模型，它在二维双曲空间的原生圆盘表示中运行，同时生成具有小世界特性、无标度度分布、高聚类性和强社区结构的网络。出于更好地理解双曲随机图的动机，我们在此引入dPSO模型，它是PSO模型到任意整数维度[公式：见原文]的推广。对所得网络的分析表明，其主要结构特性会以一种非平凡的方式受到底层双曲空间维度的影响。我们扩展后的框架不仅从理论角度来看很有趣，还可以作为已有二维双曲嵌入技术推广的起点。
