Related papers: A Quality Metric for Symmetric Graph Drawings
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
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…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
Classical Hamming graphs are Cartesian products of complete graphs, and two vertices are adjacent if they differ in exactly one coordinate. Motivated by connections to unitary Cayley graphs, we consider a generalization where two vertices…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected values. We call graphs with this property for all subgraphs with…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs. Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
In this work, we investigate the analysis of generators for dynamic graphs, which are defined as graphs whose topology changes over time. We introduce a novel concept, called ''sustainability,'' to qualify the long-term evolution of dynamic…
We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
We consider the size and structure of the automorphism groups of a variety of empirical `real-world' networks and find that, in contrast to classical random graph models, many real-world networks are richly symmetric. We relate automorphism…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…