Related papers: The hyperbolic geometry of financial networks
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…
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…
Network data is ubiquitous in various scientific disciplines, including sociology, economics, and neuroscience. Latent space models are often employed in network data analysis, but the geometric effect of latent space curvature remains a…
Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics -- a grand-challenge open problem. Here, we show…
A remarkable approach for grasping the relevant statistical features of real networks with the help of random graphs is offered by hyperbolic models, centred around the idea of placing nodes in a low-dimensional hyperbolic space, and…
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…
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…
Hyperbolic network models have gained considerable attention in recent years, mainly due to their capability of explaining many peculiar features of real-world networks. One of the most widely known models of this type is the…
Network measures that reflect the most salient properties of complex large-scale networks are in high demand in the network research community. In this paper we adapt a combinatorial measure of negative curvature (also called hyperbolicity)…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
The self-similarity of complex systems has been studied intensely across different domains due to its potential applications in system modeling, complexity analysis, etc., as well as for deep theoretical interest. Existing studies rely on…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…
The hyperbolic network models exhibit very fundamental and essential features, like small-worldness, scale-freeness, high-clustering coefficient, and community structure. In this paper, we comprehensively explore the presence of an…
Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We…
Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The…
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…
Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption 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…