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

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, reproducing strong clustering and scale-free degree distribution, 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 to confer to the PSO also a community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have 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 that, differently from GPA, forces heterogeneous angular node attractiveness 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 to explicitly fix the number and size of communities; it allows to tune their mixing property through the network temperature; it is efficient to generate networks with high clustering. After several tests we propose the nPSO as a valid and efficient model to generate networks with communities in the hyperbolic space, which can be adopted as a realistic benchmark for different tasks such as community detection and link prediction

Latent Geometry Inspired Graph Dissimilarities Enhance Affinity Propagation Community Detection in Complex Networks

Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex networks have been attaining results very far from the state of the art methods such as Infomap and Louvain. Yet, all these studies agreed that the crucial problem is to convert the unweighted network topology in a 'smart-enough' node dissimilarity matrix that is able to properly address the message passing procedure behind affinity propagation clustering. Here we introduce a conceptual innovation and we discuss how to leverage network latent geometry notions in order to design dissimilarity matrices for affinity propagation community detection. Our results demonstrate that the latent geometry inspired dissimilarity measures we design bring affinity propagation to equal or outperform current state of the art methods for community detection. These findings are solidly proven considering both synthetic 'realistic' networks (with known ground-truth communities) and real networks (with community metadata), even when the data structure is corrupted by noise artificially induced by missing or spurious connectivity

The hidden geometry of the brain

The human brain connectome is a topologically complex, spatially embedded network. One of the characteristic, basic, nonrandom rules on which brain topology relies on is the tendency of brain networks nodes to cluster into modules with high efficiency and short path length, thus reflecting an intrinsic small-world behavior, functionally segregated (local clustering) and integrated (global efficiency) [1]. Although network topology seems to be somehow connected to network geometry, one of the most challenging issues of the current network science is to infer the hidden geometry from the mere topology of a complex network. Here in, aiming at disclosing the latent geometry of the brain, we apply coalescent embedding – a novel advanced technique able to map a given network in the hyperbolic space inferring the node angular coordinates - on different structural brain networks [2]. Interestingly, we show that we can unsupervisedly reconstruct the intrinsic brain geometry with an incredible level of accuracy and that it strongly resembles the known brain anatomy. As a matter of fact, the first rule of organization of brain networks emerging in the hyperbolic space is their structural segregation into two distinct sections corresponding to the left and right hemispheres, which is a simple concept yet quite neglected in previous studies on brain connectomics. In addition, we demonstrate that the human structural brain networks exhibited a significant different geometry in two age range-specific groups. Finally, we show that the intrinsic geometry of Parkinson’s Disease patients is significantly altered compared to the healthy subjects as revealed by two novel latent geometry markers. The present study may bridge the gap between brain networks topology and geometry and may open a completely new scenario towards the realization of latent geometry network markers for the evaluation of brain disorders

“Stealing fire or stacking knowledge” by machine intelligence to model link prediction in complex networks

Summary: Current methodologies to model connectivity in complex networks either rely on network scientists’ intelligence to discover reliable physical rules or use artificial intelligence (AI) that stacks hundreds of inaccurate human-made rules to make a new one that optimally summarizes them together. Here, we provide an accurate and reproducible scientific analysis showing that, contrary to the current belief, stacking more good link prediction rules does not necessarily improve the link prediction performance to nearly optimal as suggested by recent studies. Finally, under the light of our novel results, we discuss the pros and cons of each current state-of-the-art link prediction strategy, concluding that none of the current solutions are what the future might hold for us. Future solutions might require the design and development of next generation “creative” AI that are able to generate and understand complex physical rules for us