Related papers: Recognizing Visibility Graphs of Triangulated Irre…
Let $G$ be an $n$-node planar graph. In a visibility representation of $G$, each node of $G$ is represented by a horizontal line segment such that the line segments representing any two adjacent nodes of $G$ are vertically visible to each…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
Ensuring electricity grid reliability becomes increasingly challenging with the shift towards renewable energy and declining conventional capacities. Distribution System Operators (DSOs) aim to achieve grid reliability by verifying the n-1…
In this work, a novel model of the random geometric graph (RGG), namely the isotropic random geometric graph (IRGG) has been developed and its topological properties in two dimensions have been studied in details. The defining…
The thinness of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Many NP-complete problems can be solved in polynomial time for graphs with bounded thinness,…
Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…
Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit…
Graph neural networks (GNN) rely on graph operations that include neural network training for various graph related tasks. Recently, several attempts have been made to apply the GNNs to functional magnetic resonance image (fMRI) data.…
Network visualization has established as a key complement to network analysis since the large variety of existing network layouts are able to graphically highlight different properties of networks. However, signed networks, i.e., networks…
A mixed graph $G$ is a graph that consists of both undirected and directed edges. An orientation of $G$ is formed by orienting all the undirected edges of $G$, i.e., converting each undirected edge $\{u,v\}$ into a directed edge that is…
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…
Graph Neural Networks (GNNs) excel in delineating graph structures in diverse domains, including community analysis and recommendation systems. As the interpretation of GNNs becomes increasingly important, the demand for robust baselines…
Suppose we have an arrangement $\mathcal{A}$ of $n$ geometric objects $x_1, \dots, x_n \subseteq \mathbb{R}^2$ in the plane, with a distinguished point $p_i$ in each object $x_i$. The generalized transmission graph of $\mathcal{A}$ has…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Interpretable Graph Neural Networks (GNNs) aim to reveal the underlying reasoning behind model predictions, attributing their decisions to specific subgraphs that are informative. However, existing subgraph-based interpretable methods…
We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex $u$ is represented by a geometric object $R(u)$ and in which each edge $(u,v)$ is represented…
A geometric graph is a graph drawn in the plane so that its vertices and edges are represented by points in general position and straight line segments, respectively. A vertex of a geometric graph is called pointed if it lies outside of the…
Documenting networks is an essential tool for troubleshooting network problems. The documentation details a network's structure and context, serves as a reference and makes network management more effective. Complex network diagrams are…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
A convex geometric graph is a graph whose vertices are the corners of a convex polygon P in the plane and whose edges are boundary edges and diagonals of the polygon. It is called triangulation-free if its non-boundary edges do not contain…