Related papers: New Techniques for Graph Edit Distance Computation
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
In modern relational machine learning it is common to encounter large graphs that arise via interactions or similarities between observations in many domains. Further, in many cases the target entities for analysis are actually signals on…
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which…
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.…
Graph distance metric learning serves as the foundation for many graph learning problems, e.g., graph clustering, graph classification and graph matching. Existing research works on graph distance metric (or graph kernels) learning fail to…
We improve the best known upper bound on the number of edges in a unit-distance graph on $n$ vertices for each $n\in\{16,\ldots,30\}$. When $n\leq 21$, our bounds match the best known lower bounds, and we fully enumerate the densest…
This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph $G$ and a set of terminal pairs $P$ and asks whether $G$ contains a set of pairwise edge-disjoint paths connecting every terminal…
In this paper, we present a novel error measure to compare a segmentation against ground truth. This measure, which we call Tolerant Edit Distance (TED), is motivated by two observations: (1) Some errors, like small boundary shifts, are…
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…
The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem…
Given a graph $G=(V,E)$, a set $S\subseteq V$ is said to be a monitoring edge-geodetic set if the deletion of any edge in the graph results in a change in the distance between at least one pair of vertices in $S$. The minimum size of such a…
Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the…
Many modern data analysis algorithms either assume or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimension reduction. As real data…
Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…
Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing…
Graph neural networks (GNNs) are important tools for transductive learning tasks, such as node classification in graphs, due to their expressive power in capturing complex interdependency between nodes. To enable graph neural network…
Graph anomaly detection (GAD) aims to identify anomalous graphs that significantly deviate from other ones, which has raised growing attention due to the broad existence and complexity of graph-structured data in many real-world scenarios.…
Graphs, consisting of vertices and edges, are vital for representing complex relationships in fields like social networks, finance, and blockchain. Visualizing these graphs helps analysts identify structural patterns, with readability…
Graph Anomaly Detection (GAD) is a critical task in graph machine learning with vital applications in financial fraud detection and social platform governance. However, existing GAD benchmarks are often restricted to small-scale, curated…