Related papers: New Techniques for Graph Edit Distance Computation
A monitoring edge-geodetic set, or simply an MEG-set, of a graph $G$ is a vertex subset $M \subseteq V(G)$ such that given any edge $e$ of $G$, $e$ lies on every shortest $u$-$v$ path of $G$, for some $u,v \in M$. The monitoring…
Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
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…
We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Many modern data analysis algorithms either assume that or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimensionality reduction.…
Recently, there has been a surge of interest in employing neural networks for graph generation, a fundamental statistical learning problem with critical applications like molecule design and community analysis. However, most approaches…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…
Graph anomaly detection (GAD), which aims to identify unusual graph instances (nodes, edges, subgraphs, or graphs), has attracted increasing attention in recent years due to its significance in a wide range of applications. Deep learning…
An edge-operation on a graph $G$ is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs $\mathcal{G}$, the editing distance from $G$ to $\mathcal{G}$ is the smallest number…
Subgraph matching is to find all subgraphs in a data graph that are isomorphic to an existing query graph. Subgraph matching is an NP-hard problem, yet has found its applications in many areas. Many learning-based methods have been proposed…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
Graph anomaly detection (GAD) is a vital task in graph-based machine learning and has been widely applied in many real-world applications. The primary goal of GAD is to capture anomalous nodes from graph datasets, which evidently deviate…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…