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

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 popularitysimilarity-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.

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

“…These results suggest that realistic community structure is properly reproduced by the model and the nPSO might be employed in future studies as a benchmark for testing community detection algorithms. On this regard, we propose a second study that discusses how to leverage the nPSO model to test and compare the performance of different algorithms for community detection and also link prediction [26].…”

“…To conclude, we propose the nPSO model as a valid framework able to efficiently generate realistic networks with a fixed number of communities according to a nonuniform node-angular probability distribution. The nPSO might be adopted, among the many possibilities, as a null model for the hyperbolic embedding of networks with community structure, or as a benchmark for testing community detection and link prediction algorithms, as we illustrate and discuss in a second study dedicated to this topic [26].…”

“…In addition, the Louvain algorithm has been regarded as one of the most effective algorithms for community detection in previous studies across many real and synthetic datasets [23][24][25]. However, the fact that here we tested the community detectability of the nPSO synthetic networks using only the Louvain algorithm is overcome in a second study where we compare the performance of several stateof-the-art algorithms for community detection across different parameters of the nPSO model [26].…”

Modelling Self-Organization in Complex Networks Via a Brain-Inspired Network Automata Theory Improves Link Reliability in Protein Interactomes

“…On this regard, a first solution could be to adopt the duplication-mutation/divergence model which was specifically created 64 and further developed 65 for protein networks, although a recent study spotted that it presents many limitations 66 . Another solution could be to adopt new classes of soft random geometrical graphs, such as the nonuniform-popularity-similarity-optimization model 67 , 68 , that allow a fine tuning of many network features such as clustering, small-wordness, node heterogeneity, rich-clubness and community structure. Yet, the limitation of using generative models for generation of synthetic protein interactome is that nobody know the authentic generative model behind these networks, therefore it is better to fairly compare the performance using diverse types and classes of generative models, in the hope to converge to results that resemble the ones observed using real networks.…”

Link persistence and conditional distances in multiplex networks

“…All considered models (H 2 , GMM, GMM-LP) use for simplicity a uniform distribution for the angular similarity coordinates. This leads to generated topologies without community structure [7,46,47]. On the other hand, the considered real layers (Table I) exhibit community structure and trans-layer community correlations, which are manifested in their embeddings as groups of nodes that are similar-close along the angular similarity direction-in both layers simultaneously [14,48].…”