Related papers: Complex Networks in the Framework of Nonassociativ…
We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…
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…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
A general scheme for detecting and analyzing topological patterns in large complex networks is presented. In this scheme the network in question is compared with its properly randomized version that preserves some of its low-level…
We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of…
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…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…
Motivated by the empirical analysis of the air transportation system, we define a network model that includes geographical attributes along with topological and weight (traffic) properties. The introduction of geographical attributes is…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter…
The Renormalization Group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…