The investigation of the latent geometrical space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarity-optimization (PSO) generative model is able to grow random geometric graphs in the hyperbolic space with realistic properties such as clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex systems, which is the community organization. Here, we introduce the nonuniform PSO (nPSO) generative model, a generalization of the PSO model with a tailored community structure, and we provide an efficient algorithmic implementation with a O(EN) time complexity, where N is the number of nodes and E the number of edges. Meanwhile, in recent years, the inverse problem has also gained increasing attention: given a network topology, how to provide an accurate mapping into its latent geometrical space. Unlike previous attempts based on a computationally expensive maximum likelihood optimization (whose time complexity is between O(N^3) and O(N^4)), here we show that a class of methods based on nonlinear dimensionality reduction can solve the problem with higher precision and reducing the time complexity to O(N^2).
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:34911 |
| Date | 12 August 2019 |
| Creators | Muscoloni, Alessandro |
| Contributors | Cannistraci, Carlo Vittorio, Schroeder, Michael, Mangioni, Giuseppe, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 10.1038/s41467-017-01825-5, 10.1088/1367-2630/aac06f, 10.1088/1367-2630/aac6f9, 10.1038/s41467-017-01825-5, 10.1088/1367-2630/aac06f, 10.1088/1367-2630/aac6f9 |
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