Abstract
Advances in network geometry pointed out that structural properties observed in networks derived from real complex systems can emerge in the hyperbolic space (HS). The nonuniform popularity-similarity-optimization (nPSO) is a generative model recently introduced in order to grow random geometric graphs in the HS, reproducing networks that have realistic features such as high clustering, small-worldness, scale-freeness and rich-clubness, with the additional possibility to control the community organization. Generative models allowing to tune the structural properties of ‘realistic’ synthetic networks are fundamental, because they offer a ground truth to investigate how predictive algorithms react to controlled topological variations. Here, we discuss how to leverage the nPSO model as a synthetic benchmark to compare the performance of methods for community detection and link prediction; and we prove that the nPSO offers a reliable and realistic testing framework which can complement other existing benchmarks not based on latent geometry. Furthermore, we confirm that network embedding information can improve community detection, whereas boosting link prediction in HS still needs further investigations. Indeed, we find that the presence of communities in nPSO significantly modifies the performance of link predictors and is fundamental for the reproducibility of results observed on real networks. The nPSO can trigger valuable insights to understand the intrinsic rules of link-growth and self-organization that connect topology to geometry and that are encoded in link prediction algorithms differentiating their performance.
Highlights
In recent years the study of hidden geometrical spaces behind complex network topologies has led to several developments and, currently, the hyperbolic space seems to be one of the most appropriate in order to explain many of the structural features observed in real networks [1]– [8]
Since these first examples suggested that the networks generated by the nonuniform PSO (nPSO) model could be adopted as an interesting benchmark for investigations on community detection, we compared the performance of different community detection algorithms on nPSO networks
Recent studies presented the hyperbolic disk as an adequate space to describe the latent geometry of real complex networks and the PSO model was introduced to generate random geometric graphs in the hyperbolic space, reproducing strong clustering and a scale-free degree distribution [5]
Summary
In recent years the study of hidden geometrical spaces behind complex network topologies has led to several developments and, currently, the hyperbolic space seems to be one of the most appropriate in order to explain many of the structural features observed in real networks [1]– [8]. Networks generated through the PSO model exhibit strong clustering and a scale-free degree distribution, two among the peculiar properties that usually characterize real-world topologies [9]–[11] Another important feature commonly observed is the community structure [12]–[14], which is lacking in the PSO model. The reason is that the nodes are arranged over the angular coordinate space according to a uniform distribution, since the connection probabilities are inversely proportional to the hyperbolic distances, there are not angular regions containing a cluster of spatially close nodes that are more densely connected between each other than with the rest of the network This issue has been addressed in a following study by Zuev et al [15], introducing the geometric preferential attachment (GPA). For this reason we here introduce a variation of the PSO model, which we call nonuniform PSO (nPSO) model, whose key aspects are the possibility of: i) fixing the number and size of communities; ii) tuning their mixing property through the network temperature; iii) efficiently producing highly clustered realistic networks
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