Related papers: Forman curvature for directed networks
Directed networks are essential for representing complex systems, capturing the asymmetry of interactions in fields such as neuroscience, transportation, and social networks. Directionality reveals how influence, information, or resources…
$Anomaly$ $detection$ problems (also called $change$-$point$ $detection$ problems) have been studied in data mining, statistics and computer science over the last several decades in applications such as medical condition monitoring and…
Directed networks are ubiquitous and are necessary to represent complex systems with asymmetric interactions---from food webs to the World Wide Web. Despite the importance of edge direction for detecting local and community structure, it…
Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core congestion and route reliability. In this work we analyze the…
The notion of curvature on graphs has recently gained traction in the networks community, with the Ollivier-Ricci curvature (ORC) in particular being used for several tasks in network analysis, such as community detection. In this work, we…
Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied to tasks ranging from community detection to graph…
We introduce new definitions of sectional, Ricci and scalar curvature for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature…
Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks…
Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…
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…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
Based on two classical notions of curvature for curves in general metric spaces, namely the Menger and Haantjes curvatures, we introduce new definitions of sectional, Ricci and scalar curvature for networks and their higher dimensional…
Temporal networks -- sequences of time-stamped contacts among nodes -- constitute the finest-grained representation of dynamic interaction data; however, geometric and topological analyses of such networks have remained largely confined to…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
We provide an overview of Forman-Ricci curvature and persistent homology, and how their combination can be applied to the study of networks. We discuss how the usually employed augmented Forman-Ricci curvature formula, only valid for…
We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
Graph Ricci curvature is crucial as it geometrically quantifies network structure. It pinpoints bottlenecks via negative curvature, identifies cohesive communities with positive curvature, and highlights robust hubs. This guides network…