Related papers: Forman-Ricci Curvature for Hypergraphs
Graph Neural Networks (GNNs) have shown great power for learning and mining on graphs, and Graph Structure Learning (GSL) plays an important role in boosting GNNs with a refined graph. In the literature, most GSL solutions either primarily…
In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and…
We use the discrete Ollivier-Ricci graph curvature with Ricci flow to examine the intrinsic geometry of financial markets through the empirical correlation graph of the NASDAQ 100 index. Our main result is the development of a technique to…
Most graph neural networks (GNNs) are prone to the phenomenon of over-squashing in which node features become insensitive to information from distant nodes in the graph. Recent works have shown that the topology of the graph has the…
We prove diameter bounds for graphs having positive Ricci-curvature bound in Bakry-Emery sense. One result using only curvature and maximal vertex degree is sharp in case of hypercubes. The other result depends on an additional dimension…
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…
Here we study the spectral properties of an underlying weighted graph of a non-uniform hypergraph by introducing different connectivity matrices, such as adjacency, Laplacian and normalized Laplacian matrices. We show that different…
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many…
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…
Graph neural networks(GNNs) have been demonstrated to depend on whether the node effective information is sufficiently passing. Discrete curvature (Ricci curvature) is used to study graph connectivity and information propagation efficiency…
We define a new notion of total curvature, called net total curvature, for finite graphs embedded in Rn, and investigate its properties. Two guiding principles are given by Milnor's way of measuring the local crookedness of a Jordan curve…
Curvature notions on graphs provide a theoretical description of graph topology, highlighting bottlenecks and denser connected regions. Artifacts of the message passing paradigm in Graph Neural Networks, such as oversmoothing and…
Deep neural networks have proved very successful in domains where large training sets are available, but when the number of training samples is small, their performance suffers from overfitting. Prior methods of reducing overfitting such as…
The combinatorial Ricci curvature of Forman, which is defined at the edges of a CW complex, and which makes use of only the face relations of the cells in the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does not…
Hyperbolicity is a graph parameter related to how much a graph resembles a tree with respect to distances. Its computation is challenging as the main approaches consist in scanning all quadruples of the graph or using fast matrix…
Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Group interactions are prevalent in a variety of areas. Many of them, including email exchanges, chemical reactions, and bitcoin transactions, are directional, and thus they are naturally modeled as directed hypergraphs, where each hyperarc…
This paper provides a fresh view of the neural network (NN) data flow problem, i.e., identifying the NN connections that are most important for the performance of the full model, through the lens of graph theory. Understanding the NN data…