Related papers: Doubly Saturated Ramsey Graphs: A Case Study in Co…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…
Computing the size of maximum independent sets is a NP-hard problem for fixed graphs. Characterizing and designing efficient algorithms to estimate this independence number for random graphs are notoriously difficult and still largely open…
Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective…
Recently there has been increasing interest in developing and deploying deep graph learning algorithms for many tasks, such as fraud detection and recommender systems. Albeit, there is a limited number of publicly available graph-structured…
Signed networks are graphs whose edges are labelled with either a positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The concept of balance in signed graph theory…
We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for…
The study of symmetric structures is a new trend in Ramsey theory. Recently in [7], Di Nasso initiated a systematic study of symmetrization of classical Ramsey theoretical results, and proved a symmetric version of several Ramsey theoretic…
Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only…
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining…
Block graphs are graphs in which every block (biconnected component) is a clique. A graph $G=(V,E)$ is said to be an (unpartitioned) $k$-probe block graph if there exist $k$ independent sets $N_i\subseteq V$, $1\le i\le k$, such that the…
Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs, but it is not clear that they exploit their full capacity for all inputs. We introduce the s-Trace method…
We propose a novel framework that leverages LLMs for full causal graph discovery. While previous LLM-based methods have used a pairwise query approach, this requires a quadratic number of queries which quickly becomes impractical for larger…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
One critical issue with large language models (LLMs) is their inability to guarantee correctness. Although this problem can be addressed by applying LLMs to formal rewrite systems, current LLMs are still far from adequate to generate sound…
In network tomography, one goal is to identify a small set of failed links in a network, by sending a few packets through the network and seeing which reach their destination. This problem can be seen as a variant of combinatorial group…
The size Ramsey number of a graph $H$ is defined as the minimum number of edges in a graph $G$ such that there is a monochromatic copy of $H$ in every two-coloring of $E(G)$. The size Ramsey number was introduced by Erd\H{o}s, Faudree,…
Causal graph recovery is traditionally done using statistical estimation-based methods or based on individual's knowledge about variables of interests. They often suffer from data collection biases and limitations of individuals' knowledge.…
Ramsey's theorem, concerning the guarantee of certain monochromatic patterns in large enough edge-coloured complete graphs, is a fundamental result in combinatorial mathematics. In this work, we highlight the connection between this…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…