Related papers: Network Geometry
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…
Networks are structures that encode relationships between pairs of elements or nodes. However, there is no imposed connection between these relationships, i.e., the relationship between two nodes can be independent of every other one in the…
Despite the abundance of bipartite networked systems, their organizing principles are less studied, compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result…
Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, we can therefore better understand its encompassing urban system. This study offers a geometrical approach towards…
Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and…
This paper presents methods to compare networks where relationships between pairs of nodes in a given network are defined. We define such network distance by searching for the optimal method to embed one network into another network, prove…
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…
Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural…
We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their…
Street networks, as one of the oldest infrastructures of transport in the world, play a significant role in modernization, sustainable development, and human daily activities in both ancient and modern times. Although street networks have…
Based on solid theoretical foundations, we present strong evidences that a number of real-life networks, taken from different domains like Internet measurements, biological data, web graphs, social and collaboration networks, exhibit…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little…
Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative…