2017/07/23 by Alessandro Muscoloni, Carlo Vittorio Cannistraci · 4 citations
Computer Science · Mathematics · Physics and Astronomy · Social Sciences · #Algorithm #Artificial intelligence #Cluster analysis #Clustering coefficient #Combinatorics #Complex Network Analysis Techniques #Computer science #Evolutionary Game Theory and Cooperation #Mathematics #Metric (unit) #Node (physics) #Opinion Dynamics and Social Influence #Physics #Similarity (geometry) #Space (punctuation) #Statistical physics #Topology (electrical circuits) #cond-mat.dis-nn #cs.SI #physics.soc-ph
paper · pdf · doi:10.1088/1367-2630/aac06f
published as New J. Phys. 20, 052002 (2018); New J. Phys. 20 063022 (2018)
arxiv created 2017/07/23 · openalex publication_date 2018/04/26 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The investigation of the hidden metric 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) model simulates how random geometric graphs grow in the hyperbolic space, generating realistic networks with clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex networks, which is the community organization. The geometrical-preferential-attachment (GPA) model was recently developed in order to confer to the PSO also a soft community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have a variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model. Differently from GPA, the nPSO generates synthetic networks in the hyperbolic space where heterogeneous angular node attractiveness is forced by sampling the angular coordinates from a tailored nonuniform probability distribution (for instance a mixture of Gaussians). The nPSO differs from GPA in other three aspects: it allows one to explicitly fix the number and size of communities; it allows one to tune their mixing property by means of the network temperature; it is efficient to generate networks with high clustering. Several tests on the detectability of the community structure in nPSO synthetic networks and wide investigations on their structural properties confirm that the nPSO is a valid and efficient model to generate realistic complex networks with communities.