Related papers: Hyperbolic Geometry of Complex Networks
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,…
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…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
In the framework of on nonassociative geometry, we introduce a new effective model that extends the statistical treatment of complex networks with hidden geometry. The small-world property of the network is controlled by nonlocal curvature…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
In the last decades, the study of models for large real-world networks has been a very popular and active area of research. A reasonable model should not only replicate all the structural properties that are observed in real world networks…
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…
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 show that complex (scale-free) network topologies naturally emerge from hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient greedy forwarding in these networks. Greedy forwarding is topology-oblivious.…
In the past decade, geometric network models have received vast attention in the literature. These models formalize the natural idea that similar vertices are likely to connect. Because of that, these models are able to adequately capture…
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
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…
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…
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…
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…
Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
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…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…