Related papers: Geometric Sampling of Networks
This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics…
Using Banchoff's discrete Morse Theory, in tandem with Bloch's result on the strong connection between the former and Forman's Morse Theory, and our own previous algorithm based on the later, we show that there exists a curvature-based,…
The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as…
Describing the basic properties of road network systems, such as their robustness, vulnerability, and reliability, has been a very important research topic in the field of urban transportation. Current research mainly uses several…
Characterizing shapes of high-dimensional objects via Ricci curvatures plays a critical role in many research areas in mathematics and physics. However, even though several discretizations of Ricci curvatures for discrete combinatorial…
Ricci curvature is a fundamental concept in differential geometry for encoding local geometric structure, and its graph-based analogues have recently gained prominence as practical tools for reweighting, pruning, and reshaping network…
We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by\cite{NLLG} in which the discrete time Ricci flow algorithm has been applied successfully as a…
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…
Let $M$ denote a low-dimensional manifold embedded in Euclidean space and let ${X}= \{ x_1, \dots, x_n \}$ be a collection of points uniformly sampled from it. We study the relationship between the curvature of a random geometric graph…
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Even though there exist numerous nonequivalent definitions of graph curvature, none is known to converge in any limit to any traditional…
Graph Neural Networks are highly effective at learning from relational data, leveraging node and edge features while maintaining the symmetries inherent to graph structures. However, many real-world systems, such as social or biological…
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…
This study introduces the Lower Ricci Curvature (LRC), a novel, scalable, and scale-free discrete curvature designed to enhance community detection in networks. Addressing the computational challenges posed by existing curvature-based…
Graph neural networks (GNNs) have achieved great success in many graph-based tasks. Much work is dedicated to empowering GNNs with the adaptive locality ability, which enables measuring the importance of neighboring nodes to the target node…
While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently. Those include the inability to accurately leverage…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
The identification of vertices that play a central role in network analysis is a fundamental challenge. Although traditional centrality measures have been extensively employed for this purpose, the increasing complexity of modern networks…
In this work, we propose to utilize discrete graph Ricci flow to alter network entropy through feedback control. Given such feedback input can reverse entropic changes, we adapt the moniker of Maxwells Demon to motivate our approach. In…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
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…