相关论文: An edge centrality measure based on the Kemeny con…

The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively…

We introduce weak oddness $\omega_{\textrm w}$, a new measure of uncolourability of cubic graphs, defined as the least number of odd components in an even factor. For every bridgeless cubic graph $G$, $\rho(G)\le\omega_{\textrm…

We define a general notion of a smooth invariant (central) ergodic measure on the space of paths of an $N$-graded graph (Bratteli diagram). It is based on the notion of standardness of the tail filtration in the space of paths, and the…

In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…

Given a connected graph $G(V, E)$, the edge dimension, denoted $\mathrm{edim}(G)$, is the least size of a set $S \subseteq V$ that distinguishes every pair of edges of $G$, in the sense that the edges have pairwise distinct tuples of…

Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…

We introduce a novel method, called Dispersion Entropy for Graph Signals, $DE_G$, as a powerful tool for analysing the irregularity of signals defined on graphs. We demonstrate the effectiveness of $DE_G$ in detecting changes in the…

In this paper, we address problems related to parameters concerning edge mappings of graphs. Inspired by Ramsey's Theorem, the quantity $m(G, H)$ is defined to be the minimum number $n$ such that for every $f: E(K_n) \rightarrow E(K_n)$…

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…

Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were…

Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of…

Core decomposition is an efficient building block for various graph analysis tasks such as dense subgraph discovery and identifying influential nodes. One crucial weakness of the core decomposition is its sensitivity to changes in the…

Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural…

Given a connected graph $G$, the metric (resp. edge metric) dimension of $G$ is the cardinality of the smallest ordered set of vertices that uniquely identifies every pair of distinct vertices (resp. edges) of $G$ by means of distance…

Let $G(V, E)$ be a connected simple undirected graph. In this paper we prove that the edge metric dimension (introduced by Kelenc, Tratnik and Yero) of the Erd\H{o}s-R\'enyi random graph $G(n, p)$ is given by: $$\textrm{edim}(G(n, p)) = (1…

Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…

Centrality measures, erstwhile popular amongst the sociologists and psychologists, have seen broad and increasing applications across several disciplines of late. Amongst a plethora of application specific definitions available in the…

Centrality metrics have been widely applied to identify the nodes in a graph whose removal is effective in decomposing the graph into smaller sub-components. The node--removal process is generally used to test network robustness against…

This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the…

Here we present a range-limited approach to centrality measures in both non-weighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on…