相关论文: An edge centrality measure based on the Kemeny con…
The concept of a monitoring edge-geodetic set (MEG-set) in a graph $G$, denoted $MEG(G)$, refers to a subset of vertices $MEG(G)\subseteq V(G)$ such that every edge $e$ in $G$ is monitored by some pair of vertices $ u, v \in MEG(G)$, where…
Betweenness centrality is a widely-used measure in the analysis of large complex networks. It measures the potential or power of a vertex to control the communication over the network under the assumption that information primarily flows…
In 2010, Joyce et. al defined the leverage centrality of vertices in a graph as a means to analyze functional connections within the human brain. In this metric a degree of a vertex is compared to the degrees of all it neighbors. We…
An edge irregular total $k$-labelling $f : V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ of a graph $G$ is a labelling of the vertices and the edges of $G$ in such a way that any two different edges have distinct weights. The weight of an edge…
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…
In a social network, the strength of relationships between users can significantly affect the stability of the network. In this paper, we use the k-truss model to measure the stability of a social network. To identify critical connections,…
Spanning Centrality is a measure used in network analysis to determine the importance of an edge in a graph based on its contribution to the connectivity of the entire network. Specifically, it quantifies how critical an edge is in terms of…
Dominating sets and resolving sets have important applications in control theory and computer science. In this paper, we introduce an edge-analog of the classical dominant metric dimension of graphs. By combining the concepts of a…
The betweenness centrality (BC) is an important quantity for understanding the structure of complex large networks. However, its calculation is in general difficult and known in simple cases only. In particular, the BC has been exactly…
We introduce a new method for decomposing the edge set of a graph, and use it to replace the Regularity lemma of Szemer\'edi in some graph embedding problems. An algorithmic version is also given.
A concentration of measure result is proved for the number of isolated vertices $Y$ in the Erd\H{o}s-R\'{e}nyi random graph model on $n$ edges with edge probability $p$. When $\mu$ and $\sigma^2$ denote the mean and variance of $Y$…
We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown.…
We consider the incremental computation of the betweenness centrality of all vertices in a large complex network modeled as a graph G = (V, E), directed or undirected, with positive real edge-weights. The current widely used algorithm to…
The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. By appropriately introducing a weight to each edge of a graph, we determine, among other thing, the skewness of the generalized Petersen…
The tau constant is an important invariant of a metrized graph, and it has applications in arithmetic properties of curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We…
We present a simple model to predict network activity at the edge level, by extending a known approximation method to compute Betweenness Centrality (BC) with a repulsive mechanism to prevent unphysical densities. By taking into account the…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graph neural networks (GNNs) have achieved great success on various tasks and fields that require relational modeling. GNNs aggregate node features using the graph structure as inductive biases resulting in flexible and powerful models.…
A nonuniform version of the Berry-Esseen bound has been proved. The most important feature of the new bound is a monotonically decreasing function C(|t|) instead of the universal constant C=29.1174: C(|t|)<C if |t| > 3.2, and C(|t|) tends…
Edge centrality measures are functions that evaluate the importance of edges in a network. They can be used to assess the role of a backlink for the popularity of a website as well as the importance of a flight in virus spreading. Various…