Growing hyperbolic networks beyond two dimensions: the generalised popularity-similarity optimisation model
arXiv:2108.03328 · doi:10.1038/s41598-021-04379-1
Abstract
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 PSO model, a generalisation of the PSO model to any arbitrary integer dimension . 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.
arXiv comment65 pages, 30 figures. arXiv admin note: text overlap with arXiv:2101.02249
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