相关论文: Graph Edit Distance with General Costs Using Neura…

The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph…

For any fixed positive integer $r$ and a given budget $k$, the $r$-\textsc{Eigenvalue Vertex Deletion} ($r$-EVD) problem asks if a graph $G$ admits a subset $S$ of at most $k$ vertices such that the adjacency matrix of $G\setminus S$ has at…

The edit distance between two graphs on the same labeled vertex set is the size of the symmetric difference of the edge sets. The distance between a graph, $G$, and a hereditary property, ${\cal H}$, is the minimum of the distance between…

We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two…

The editing of a combinatorial object is the alteration of some of its elements such that the resulting object satisfies a certain fixed property. The edit problem for graphs, when the edges are added or deleted, was first studied…

Recently, a new way of avoiding crossings in straight-line drawings of non-planar graphs has been investigated. The idea of partial edge drawings (PED) is to drop the middle part of edges and rely on the remaining edge parts called stubs.…

The rise of graph representation learning as the primary solution for many different network science tasks led to a surge of interest in the fairness of this family of methods. Link prediction, in particular, has a substantial social…

The graph traversal edit distance (GTED), introduced by Ebrahimpour Boroojeny et al.~(2018), is an elegant distance measure defined as the minimum edit distance between strings reconstructed from Eulerian trails in two edge-labeled graphs.…

Diverse explainability methods of graph neural networks (GNN) have recently been developed to highlight the edges and nodes in the graph that contribute the most to the model predictions. However, it is not clear yet how to evaluate the…

Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant…

Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…

Graph unlearning, which involves deleting graph elements such as nodes, node labels, and relationships from a trained graph neural network (GNN) model, is crucial for real-world applications where data elements may become irrelevant,…

The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…

Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged at each…

Graph Neural Networks (GNNs) traditionally employ a message-passing mechanism that resembles diffusion over undirected graphs, which often leads to homogenization of node features and reduced discriminative power in tasks such as node…

Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…

Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…

We pursue the study of edge-irregulators of graphs, which were recently introduced in [Fioravantes et al. Parametrised Distance to Local Irregularity. IPEC, 2024]. That is, we are interested in the parameter Ie(G), which, for a given graph…

Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…

Data augmentation plays a critical role in improving model performance across various domains, but it becomes challenging with graph data due to their complex and irregular structure. To address this issue, we propose EPIC (Edit Path…