A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

Abstract

2 Brain bio-inspired computing (BBC) lab, IRCCS Centro Neurolesi 'Bonino Pulejo', Messina, Italy E-mail: kalokagathos.agon@gmail.com Keywords: network models, hyperbolic geometry, community structure Supplementary material for this article is available online AbstractThe 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-similarityoptimization (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.

Local-community network automata modelling based on length-three-paths for prediction of complex network structures in protein interactomes, food webs and more

“…The natural follow up is to build synthetic networks on which we could change the average degree, average clustering and replicate the contradictory results obtained on real networks. Therefore, we performed also link prediction on synthetic networks generated with the nonuniform popularity-similarity-optimization model (nPSO) [17], [18], which is a recently introduced random geometrical graph generative model that allows to build networks in the hyperbolic space with clustering, small-worldness, scale-freeness, rich-clubness and a tailored community structure. We fixed the size to 1000 nodes and the exponent of the power-law degree distribution to 3.…”

Leveraging the nonuniform PSO network model as a benchmark for performance evaluation in community detection and link prediction

“…table 6, whereas the PSO and nPSO networks, at least in their basic implementation, are designed to follow a power-law degree distribution. We emphasize that in the other study in which we theoretically introduce and discuss the nPSO model [20], it has been numerically proven that changing or removing the community structure in the nPSO networks (while keeping fixed the other model parameters) does not significantly affect the main structural features of the network, like clustering coefficient, characteristic path length, power-law exponent, assortativity and LCP-correlation [20]. Looking at the large-size networks, which tend to be scale-free (see suppl.…”

“…However, real networks exhibit another very important feature that is community organization, not contemplated in the original PSO model. For such reason, Muscoloni et al [20] introduced a variation of it, the nonuniform PSO (nPSO) model, which allows to explicitly control the number of communities, their size and mixing property. Providing a benchmark for community detection requires the possibility to manipulate structural properties such as average node degree, clustering, small-worldness and scale-freeness, in order to assess how differently community detection algorithms react to these controlled topological variations.…”

Link Prediction based on Quantum-Inspired Ant Colony Optimization

“…The first group composes of two synthetic networks that are Watts-Strogatz (WS)’s small-world network 43 and Cannistraci’s nonuniform popularity-similarity optimization (nPSO) network 44 . The WS small-world network is generated by rewiring r  * | E | links on a regular lattice with n nodes, where r denotes the randomized rewiring probability and | E | denotes the total number of links 45,46 .…”

“…The WS small-world network is generated by rewiring r  * | E | links on a regular lattice with n nodes, where r denotes the randomized rewiring probability and | E | denotes the total number of links 45,46 . The nPSO model 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, and the nPSO model allows to explicitly control the size, the mixing property and the number of communities of the generated network 47 .…”