Related papers: Benchmarks of Extended Basis Reachability Graphs
With the growing use of deep learning methods, particularly graph neural networks, which encode intricate interconnectedness information, for a variety of real tasks, there is a necessity for explainability in such settings. In this paper,…
The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and…
Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ…
We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes…
Graphs provide a powerful representation formalism that offers great promise to benefit tasks like handwritten signature verification. While most state-of-the-art approaches to signature verification rely on fixed-size representations,…
The growing interest in making use of Knowledge Graphs for developing explainable artificial intelligence, there is an increasing need for a comparable and repeatable comparison of the performance of Knowledge Graph-based systems. History…
A key issue in network reliability analysis. A graph with $n$ nodes and whose $e$ edges fail independently with probability $p$ is an \emph{Uniformly Most Reliable Graph} (UMRG) if it has the highest reliability among all graphs with the…
Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary…
Graph embedding is the task of representing nodes of a graph in a low-dimensional space and its applications for graph tasks have gained significant traction in academia and industry. The primary difference among the many recently proposed…
For a positive integer $k\ge 1$, a graph $G$ is $k$-stepwise irregular ($k$-SI graph) if the degrees of every pair of adjacent vertices differ by exactly $k$. Such graphs are necessarily bipartite. Using graph products it is demonstrated…
Identifying cohesive subgraphs in hypergraphs is a fundamental problem that has received recent attention in data mining and engineering fields. Existing approaches mainly focus on a strongly induced subhypergraph or edge cardinality,…
Many mathematical models have been leveraged to design embeddings for representing Knowledge Graph (KG) entities and relations for link prediction and many downstream tasks. These mathematically-inspired models are not only highly scalable…
We give the first polynomial-time, differentially node-private, and robust algorithm for estimating the edge density of Erd\H{o}s-R\'enyi random graphs and their generalization, inhomogeneous random graphs. We further prove…
Effective Resistance (ER) is a fundamental tool in various graph learning tasks. In this paper, we address the problem of efficiently approximating ER on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with $n$ vertices and $m$ edges.…
Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs,…
Retrieval-Augmented Generation (RAG) has become a core paradigm for enhancing factual grounding and multi-hop reasoning in Large Language Models (LLMs). Traditional text-based RAG often retrieves logically irrelevant pseudo-evidence, while…
Protecting sensitive program content is a critical issue in various situations, ranging from legitimate use cases to unethical contexts. Obfuscation is one of the most used techniques to ensure such protection. Consequently, attackers must…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
The current surge of interest in graph-based data models mirrors the usage of increasingly complex reachability queries, as witnessed by recent analytical studies on real-world graph query logs. Despite the maturity of graph DBMS…
Graph unlearning has emerged as a pivotal research area for ensuring privacy protection, given the widespread adoption of Graph Neural Networks (GNNs) in applications involving sensitive user data. Among existing studies, certified graph…