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Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the…
Graph neural networks (GNNs) are powerful tools on graph data. However, their predictions are mis-calibrated and lack interpretability, limiting their adoption in critical applications. To address this issue, we propose a new…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
The problem of counting occurrences of query graphs in a large data graph, known as subgraph counting, is fundamental to several domains such as genomics and social network analysis. Many important special cases (e.g. triangle counting)…
The dichromatic number of a digraph $D$ is the minimum number of colors needed to color its vertices in such a way that each color class induces an acyclic digraph. As it generalizes the notion of the chromatic number of graphs, it has been…
Structural node embeddings, vectors capturing local connectivity information for each node in a graph, have many applications in data mining and machine learning, e.g., network alignment and node classification, clustering and anomaly…
With the increasing popularity of large language models (LLMs), reasoning on basic graph algorithm problems is an essential intermediate step in assessing their abilities to process and infer complex graph reasoning tasks. Existing methods…
Let ${\rm dim}(G)$ and $D(G)$ respectively denote the metric dimension and the distinguishing number of a graph $G$. It is proved that $D(G) \le {\rm dim}(G)+1$ holds for every connected graph $G$. Among trees, exactly paths and stars…
We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…
Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
A conjecture in algorithmic model theory predicts that the model-checking problem for first-order logic is fixed-parameter tractable on a hereditary graph class if and only if the class is monadically dependent. Originating in model theory,…
In the past, the dichotomy between homophily and heterophily has inspired research contributions toward a better understanding of Deep Graph Networks' inductive bias. In particular, it was believed that homophily strongly correlates with…
Recent works on machine learning for combinatorial optimization have shown that learning based approaches can outperform heuristic methods in terms of speed and performance. In this paper, we consider the problem of finding an optimal…
Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
The $k$-dominating graph $D_k(G)$ of a graph $G$ is defined on the vertex set consisting of dominating sets of $G$ with cardinality at most $k$, two such sets being adjacent if they differ by either adding or deleting a single vertex. A…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…