Related papers: Distance Matrices for Conjugate Skew Gain Graphs
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
We study the spectrum of the join of several circulant matrices. We apply our results to compute explicitly the spectrum of certain graphs obtained by joining several circulant graphs.
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…
We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the graph distances and derive error bounds under various…
Given a distance matrix $D$, we study the behavior of its compaction vector and reduction matrix with respect to the problem of the realization of $D$ by a weighted graph. To this end, we first give a general result on realization by…
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs -- a 2014 survey by Aouchiche and Hansen on…
We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…
The adjacency-diametrical matrix (AD matrix) of a connected graph $G$ with diameter $d$, denoted by $AD(G)$, is the matrix indexed by the vertices of $G$ in which the $(i,j)$-entry of $AD(G)$ is $1$ if $d_G(v_i,v_j)=1$, is $d$ if…
A matchstick graph is a plane graph with edges drawn as unit distance line segments. This class of graphs was introduced by Harborth who conjectured that a matchstick graph on $n$ vertices can have at most $\lfloor 3n - \sqrt{12n -…
The graph edit distance (GED) is a well-established distance measure widely used in many applications. However, existing methods for the GED computation suffer from several drawbacks including oversized search space, huge memory…
In this article, the distance magic index of certain important classes of partite graphs are determined.
The spatial preferred attachment (SPA) model is a model for networked information spaces such as domains of the World Wide Web, citation graphs, and on-line social networks. It uses a metric space to model the hidden attributes of the…
The spectral excess theorem for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. A bipartite graph is distance-biregular when it is…
Due to their capacity to encode rich structural information, labeled graphs are often used for modeling various kinds of objects such as images, molecules, and chemical compounds. If pattern recognition problems such as clustering and…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
Let $G$ be a simple graph with an orientation $\sigma$, which assigns to each edge a direction so that $G^\sigma$ becomes a directed graph. $G$ is said to be the underlying graph of the directed graph $G^\sigma$. In this paper, we define a…
A new class of distances for graph vertices is proposed. This class contains parametric families of distances which reduce to the shortest-path, weighted shortest-path, and the resistance distances at the limiting values of the family…