Related papers: Identifying Cluttering Edges in Near-Planar Graphs
We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…
In this paper we study the computational complexity of the Upward Planarity Extension problem, which takes in input an upward planar drawing $\Gamma_H$ of a subgraph $H$ of a directed graph $G$ and asks whether $\Gamma_H$ can be extended to…
Computing planar orthogonal drawings with the minimum number of bends is one of the most relevant topics in Graph Drawing. The problem is known to be NP-hard, even when we want to test the existence of a rectilinear planar drawing, i.e., an…
The performance of distributed averaging depends heavily on the underlying topology. In various fields, including compressed sensing, multi-party computation, and abstract graph theory, graphs may be expected to be free of short cycles,…
We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the ob- servation of smaller graphs and basic structure of our heuristics.…
The super edge-magicness of graphs of equal order and size has been shown to be important since such graphs can be used as seeds to answer many questions related to (super) edge-magic labelings and other types of well studied labelings, as…
Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…
A graph is $k$-planar $(k \geq 1)$ if it can be drawn in the plane such that no edge is crossed more than $k$ times. A graph is $k$-quasi planar $(k \geq 2)$ if it can be drawn in the plane with no $k$ pairwise crossing edges. The families…
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their…
Graph Neural Network (GNN) research has produced strategies to modify a graph's edges using gradients from a trained GNN, with the goal of network design. However, the factors which govern gradient-based editing are understudied, obscuring…
Discovering the underlying structure of a given graph is one of the fundamental goals in graph mining. Given a graph, we can often order vertices in a way that neighboring vertices have a higher probability of being connected to each other.…
The study of network representations of physical, biological, and social phenomena can help us better understand the structural and functional dynamics of their networks and formulate predictive models of these phenomena. However, due to…
A drawing of a graph is $k$-plane if every edge contains at most $k$ crossings. A $k$-plane drawing is saturated if we cannot add any edge so that the drawing remains $k$-plane. It is well-known that saturated $0$-plane drawings, that is,…
We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…
We prove that triangulated IC-planar and NIC-planar graphs can be recognized in cubic time. A graph is 1-planar if it can be drawn in the plane with at most one crossing per edge. A drawing is IC-planar if, in addition, each vertex is…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
Recent empirical research has indicated that human graph reading performance improves when crossing angles increase. However, crossing angle has not been used as an aesthetic criterion for graph drawing algorithms so far. In this paper, we…
A graph is IC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share no common end vertex. IC-planarity specializes both NIC-planarity, which allows a pair of crossing…
Most Graph Neural Networks (GNNs) cannot distinguish some graphs or indeed some pairs of nodes within a graph. This makes it impossible to solve certain classification tasks. However, adding additional node features to these models can…
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the…