Related papers: Discrete curvature on graphs from the effective re…

Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…

In recent years, network models have become more complex with the development of big data. Therefore, more advanced network analysis is required. In this paper, we introduce a new quantitative measure named combinatorial evaluation, which…

In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…

Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…

We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and…

We investigate whether there is a relationship between the discrete Bakry-\'{E}mery curvature of a graph and the smooth curvature of an ambient surface into which the graph is embedded geodesically. As we used weighted graphs as test…

Contrastive learning (CL) has emerged as a powerful framework for learning representations of images and text in a self-supervised manner while enhancing model robustness against adversarial attacks. More recently, researchers have extended…

We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature…

In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. In addition, the Kron reduction method is a standard tool for…

In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…

Graph neural network (GNN) has been demonstrated powerful in modeling graph-structured data. However, despite many successful cases of applying GNNs to various graph classification and prediction tasks, whether the graph geometrical…

How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…

Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the…

The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…

In this note, we provide Steinerberger curvature formulas for block graphs, discuss curvature relations between two graphs and the graph obtained by connecting them via a bridge, and show that self-centered Bonnet-Myers sharp graphs are…

It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two…

In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our…

Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…

Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.

The phenomenon of arrest of an unstably-growing crack due to a curved weak interface is investigated. The weak interface can produce the deviation of the crack path, trapping the crack at the interface, leading to stable crack growth for…