Related papers: Graph rewriting with polarized cloning

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…

There has been a recent surge in transformer-based architectures for learning on graphs, mainly motivated by attention as an effective learning mechanism and the desire to supersede handcrafted operators characteristic of message passing…

The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back…

Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…

Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}. We…

A subset $S$ of initially infected vertices of a graph $G$ is called forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbour, infects…

For a fixed graph class $\Pi$, the goal of $\Pi$-Modification is to transform an input graph $G$ into a graph $H\in\Pi$ using at most $k$ modifications. Vertex and edge deletions are common operations, and their (parameterized) complexity…

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…

Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in…

The simplest way to make a dynamical system out of a finite connected graph $G$ is to give it a polarization, that is to say a cyclic ordering of the edges incident to a vertex, for each vertex. The phase space $\mathcal{P}(G)$ then…

Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which…

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…

Monographs are graph-like structures with directed edges of unlimited length that are freely adjacent to each other. The standard nodes are represented as edges of length zero. They can be drawn in a way consistent with standard graphs and…

In this paper, we consider the problem of clustering graph nodes and sparsifying graph edges over distributed graphs, when graph edges with possibly edge duplicates are observed at physically remote sites. Although edge duplicates across…

How can we find the right graph for semi-supervised learning? In real world applications, the choice of which edges to use for computation is the first step in any graph learning process. Interestingly, there are often many types of…

Clustering a signed graph means partitioning the vertices into sets ("clusters") so that every positive edge, and no negative edge, is within a cluster. Clustering is not always possible; the obstruction is circles with exactly one negative…

Algorithms for node clustering typically focus on finding homophilous structure in graphs. That is, they find sets of similar nodes with many edges within, rather than across, the clusters. However, graphs often also exhibit heterophilous…

Cluster Editing, also known as Correlation Clustering, is a well-studied graph modification problem. In this problem, one is given a graph and the task is to perform up to $k$ edge additions or deletions to transform it into a cluster…

Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…