Related papers: Detecting the ultra low dimensionality of real net…
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…
A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
Multilayer networks offer a powerful framework for modeling complex systems across diverse domains, effectively capturing multiple types of connections and interdependent subsystems commonly found in real world scenarios. To analyze these…
In existing models and embedding methods of networked systems, node features describing their qualities are usually overlooked in favor of focusing solely on node connectivity. This study introduces $FiD$-Mercator, a model-based ultra-low…
What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common…
Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by…
Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network's low-dimensional structure, and the…
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…
Embedding a network in hyperbolic space can reveal interesting features for the network structure, especially in terms of self-similar characteristics. The hidden metric space, which can be thought of as the underlying structure of the…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
Low-dimensional embeddings, from classical spectral embeddings to modern neural-net-inspired methods, are a cornerstone in the modeling and analysis of complex networks. Recent work by Seshadhri et al. (PNAS 2020) suggests that such…