Related papers: Hamming Graph Metrics: A Multi-Scale Framework for…
Genetic sequencing has become an increasingly affordable and accessible source of genomic data in computational biology. This data is often represented as $k$-mers, i.e., strings of some fixed length $k$ with symbols chosen from a reference…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Graph generation is a crucial task in many fields, including network science and bioinformatics, as it enables the creation of synthetic graphs that mimic the properties of real-world networks for various applications. Graph Generative…
Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via…
Graph similarity learning (GSL), also referred to as graph matching in many scenarios, is a fundamental problem in computer vision, pattern recognition, and graph learning. However, previous GSL methods assume that graphs are homogeneous…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
A subset of vertices in a graph is called resolving when the geodesic distances to those vertices uniquely distinguish every vertex in the graph. Here, we characterize the resolvability of Hamming graphs in terms of a constrained linear…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
Heterogeneous graphs, which contain nodes and edges of multiple types, are prevalent in various domains, including bibliographic networks, social media, and knowledge graphs. As a fundamental task in analyzing heterogeneous graphs,…
The growing interests and applications of graph learning in diverse domains have propelled the development of a unified model generalizing well across different graphs and tasks, known as the Graph Foundation Model (GFM). Existing research…
In high-dimensional graph learning problems, some topological properties of the graph, such as bounded node degree or tree structure, are typically assumed to hold so that the sample complexity of recovering the graph structure can be…
Despite the success of Heterogeneous Graph Neural Networks (HGNNs) in modeling real-world Heterogeneous Information Networks (HINs), challenges such as expressiveness limitations and over-smoothing have prompted researchers to explore Graph…
Semantic parsing of long documents remains challenging due to quadratic growth in pairwise composition and memory requirements. We introduce \textbf{Hierarchical Segment-Graph Memory (HSGM)}, a novel framework that decomposes an input of…
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts for the maximal smallest degree of a subgraph containing a…
We introduce a new graph-theoretic concept in the area of network monitoring. A set $M$ of vertices of a graph $G$ is a \emph{distance-edge-monitoring set} if for every edge $e$ of $G$, there is a vertex $x$ of $M$ and a vertex $y$ of $G$…
Graph mining has become crucial in fields such as social science, finance, and cybersecurity. Many large-scale real-world networks exhibit both heterogeneity, where multiple node and edge types exist in the graph, and heterophily, where…
Graph edit distance / similarity is widely used in many tasks, such as graph similarity search, binary function analysis, and graph clustering. However, computing the exact graph edit distance (GED) or maximum common subgraph (MCS) between…
We present a novel theoretical framework connecting k-component edge connectivity with spectral graph theory and homology theory to pro vide new insights into the resilience of real-world networks. By extending classical edge connectivity…