Related papers: Efficient Shortest Path Algorithm Using An Unique …
In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal…
The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…
Graph Neural Networks (GNNs) have demonstrated remarkable success in various applications, yet they often struggle to capture long-range dependencies (LRD) effectively. This paper introduces GraphMinNet, a novel GNN architecture that…
Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is…
Identifying shortest paths between nodes in a network is a common graph analysis problem that is important for many applications involving routing of resources. An adversary that can manipulate the graph structure could alter traffic…
We describe a general purpose algorithm for counting simple cycles and simple paths of any length $\ell$ on a (weighted di)graph on $N$ vertices and $M$ edges, achieving a time complexity of $O\left(N+M+\big(\ell^\omega+\ell\Delta\big)…
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…
Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance…
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…
Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted…
Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps, which constructs a graph embedding…
Many networks, such as transportation, power, and water distribution, can be represented as graphs. Crucial challenge in graph representations is identifying the importance of graph edges and their influence on overall network efficiency…
Learning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis and data mining. Recent GNN…
Graph convolutional networks (GCN) have recently demonstrated their potential in analyzing non-grid structure data that can be represented as graphs. The core idea is to encode the local topology of a graph, via convolutions, into the…
A new class of distances for graph vertices is proposed. This class contains parametric families of distances which reduce to the shortest-path, weighted shortest-path, and the resistance distances at the limiting values of the family…
The goal of graph summarization is to represent large graphs in a structured and compact way. A graph summary based on equivalence classes preserves pre-defined features of a graph's vertex within a $k$-hop neighborhood such as the vertex…
Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying…
Given a fixed positive integer $k$ and a simple undirected graph $G = (V, E)$, the {\em $k^-$-path partition} problem, denoted by $k$PP for short, aims to find a minimum collection $\cal{P}$ of vertex-disjoint paths in $G$ such that each…
We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between $u$ and $v$ is the minimum of the shortest path…
The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…