Related papers: Topology Based Scalable Graph Kernels
In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we…
Graph clustering is a longstanding research topic, and has achieved remarkable success with the deep learning methods in recent years. Nevertheless, we observe that several important issues largely remain open. On the one hand, graph…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the…
Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…
The graph alignment problem explores the concept of node correspondence and its optimality. In this paper, we focus on purely geometric graph alignment methods, namely our newly proposed Ricci Matrix Comparison (RMC) and its original form,…
We introduce a novel class of explicit feature maps based on topological indices that represent each graph by a compact feature vector, enabling fast and interpretable graph classification. Using radial basis function kernels on these…
We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical…
We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…
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…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of…
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…
In colored graphs, node classes are often associated with either their neighbors class or with information not incorporated in the graph associated with each node. We here propose that node classes are also associated with topological…
We describe the design of a reproducing kernel suitable for attributed graphs, in which the similarity between the two graphs is defined based on the neighborhood information of the graph nodes with the aid of a product graph formulation.…
Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take…
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…
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-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…