Related papers: Ricci Matrix Comparison for Graph Alignment: A DMC…
The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we…
In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs $G_{1}=(V_{1},E_{1})$ and $G_{2}=(V_{2},E_{2})$, the objective is to map nodes $u, v \in G_1$ to nodes $u',v'\in G_2$ such that when $u,…
Graph embedding approaches attempt to project graphs into geometric entities, i.e, manifolds. The idea is that the geometric properties of the projected manifolds are helpful in the inference of graph properties. However, if the choice of…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We propose a new graph kernel for graph classification and comparison using Ollivier Ricci curvature. The Ricci curvature of an edge in a graph describes the connectivity in the local neighborhood. An edge in a densely connected…
Geometric matrix completion (GMC) has been proposed for recommendation by integrating the relationship (link) graphs among users/items into matrix completion (MC). Traditional GMC methods typically adopt graph regularization to impose…
Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
In recent years extensions of manifold Ricci curvature to discrete combinatorial objects such as graphs and hypergraphs (popularly called as "network shapes"), have found a plethora of applications in a wide spectrum of research areas…
Ricci curvature and its associated flow offer powerful geometric methods for analyzing complex networks. While existing research heavily focuses on applications for undirected graphs such as community detection and core extraction, there…
Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Network alignment, or the task of finding meaningful node correspondences between nodes in different graphs, is an important graph mining task with many scientific and industrial applications. An important principle for network alignment is…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
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…
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…
In a graph, a (perfect) matching cut is an edge cut that is a (perfect) matching. Matching Cut (MC), respectively, Perfect Matching Cut (PMC), is the problem of deciding whether a given graph has a matching cut, respectively, a perfect…
We present a Markov chain Monte-Carlo (MCMC) method to make a geometric graph which satisfies the following two conditions: (i) The degree of each vertex is fixed to a positive integer $k$. (ii) The probability that two vertices located on…
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…