Related papers: Continuous Average Straightness in Spatial Graphs
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
The eccentricity of a vertex $v$ in a graph $G$ is the maximum distance between $v$ and any other vertex of $G$. The diameter of a graph $G$ is the maximum eccentricity of a vertex in $G$. The eccentric connectivity index of a connected…
A new metric for quantifying pairwise vertex connectivity in graphs is defined and an implementation presented. While general in nature, it features a combination of input features well-suited for social networks, including applicability to…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
A realization of a graph $G=(V,E)$ is a map $v\colon V\to\Bbb R^d$ that assigns to each vertex a point in $d$-dimensional Euclidean space. We study graph realizations from the perspective of representation theory (expressing certain…
A unit ball graph consists of a set of vertices, labeled by points in Euclidean space, and edges joining all pairs of points within distance 1. These geometric graphs are used to model a variety of spatial networks, including communication…
Given a graph $\mathcal{G}$, the spanning centrality (SC) of an edge $e$ measures the importance of $e$ for $\mathcal{G}$ to be connected. In practice, SC has seen extensive applications in computational biology, electrical networks, and…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rough classification of large empirical graphs into families…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…
In a graph $A$, the measure $|M_g^A(f)|=m_g^A(f)$ for each arbitrary edge $f=gh$ counts the edges in $A$ closer to $g$ than $h$. $A$ is termed an edge quasi-$\lambda$-distance-balanced graph in a metric space (abbreviated as $EQDBG$), where…
The metric dimension of a graph is the cardinality of a minimum resolving set, which is the set of vertices such that the distance representations of every vertex with respect to that set are unique. A fault-tolerant metric basis is a…
A good edge-labelling of a simple graph is a labelling of its edges with real numbers such that, for any ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. Say a graph is good if it admits a good…
Graph comparison is a fundamental operation in data mining and information retrieval. Due to the combinatorial nature of graphs, it is hard to balance the expressiveness of the similarity measure and its scalability. Spectral analysis…
There are several applications that benefit from a definition of centrality which is applicable to sets of vertices, rather than individual vertices. However, existing definitions might not be able to help us in answering several network…
A new measure $c(e)$ of the centrality of an edge $e$ in an undirected graph $G$ is introduced. It is based on the variation of the Kemeny constant of the graph after removing the edge $e$. The new measure is designed in such a way that the…
The \emph{distance-number} of a graph $G$ is the minimum number of distinct edge-lengths over all straight-line drawings of $G$ in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the…
Resistance distance has been studied extensively in the past years, with the majority of previous studies devoted to undirected networks, in spite of the fact that various realistic networks are directed. Although several generalizations of…