Related papers: Continuous mean distance of a weighted graph
A strongly connected digraph is called a cactoid-type if each of its blocks is a digraph consisting of finitely many oriented cycles sharing a common directed path. In this article, we find the formula for the determinant of the distance…
For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
Graph Edit Distance (GED) is defined as the minimum cost transformation of one graph into another and is a widely adopted metric for measuring the dissimilarity between graphs. The major problem of GED is that its computation is NP-hard,…
Let $G$ be a connected graph with vertex set $V(G)$, and denote by $d_G(u,v)$ the distance from $u$ to $v$ in $G$, for any $u,v \in V(G)$. The average distance of an $n$-vertex connected graph $G$, denoted by $\mu(G)$, is defined to be the…
In several recent papers, the maximal safety distance that two players can maintain while moving through a graph has been defined and studied using three different spans of the graph, each with different movement conditions. Mainly, vertex…
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…
Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
Let $G$ be a connected graph. Given an ordered set $W = \{w_1, w_2,\dots w_k\}\subseteq V(G)$ and a vertex $u\in V(G)$, the representation of $u$ with respect to $W$ is the ordered $k$-tuple $(d(u,w_1), d(u,w_2),\dots,$ $d(u,w_k))$, where…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We…
The problem of continuation of a partially defined metric can be efficiently studied using graph theory. Let $G=G(V,E)$ be an undirected graph with the set of vertices $V$ and the set of edges $E$. A necessary and sufficient condition under…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size…
The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Inspired by Lelek's idea from [Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199 -- 214], we introduce the novel notion of the span of graphs. Using this, we solve the problem of determining the \emph{maximal safety…
Understanding and adequately assessing the difference between a true and a learnt causal graphs is crucial for causal inference under interventions. As an extension to the graph-based structural Hamming distance and structural intervention…