Related papers: Recognizing Distance-Count Matrices is Difficult
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…
The calculation of centrality measures is common practice in the study of networks, as they attempt to quantify the importance of individual vertices, edges, or other components. Different centralities attempt to measure importance in…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
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 uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this…
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…
Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…
Harmonic centrality calculates the importance of a node in a network by adding the inverse of the geodesic distances of this node to all the other nodes. Harmonic centralization, on the other hand, is the graph-level centrality score based…
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…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
The non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. The problem is even more difficult when the information is distributed across networks (e.g., communication networks in different…
Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some…
Typing Yesterday into the search-bar of your browser provides a long list of websites with, in top places, a link to a video by The Beatles. The order your browser shows its search results is a notable example of the use of network…
Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…
Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
The determination of node centrality is a fundamental topic in social network studies. As an addition to established metrics, which identify central nodes based on their brokerage power, the number and weight of their connections, and the…
We consider bounds on maximum nullity of a graph via transversal numbers of compatible collections of forts. Results include generalizations of theorems from symmetric to combinatorially symmetric matrices, special bases of matrix…
The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is…
A graph $X$ is said to be {\it distance--balanced} if for any edge $uv$ of $X$, the number of vertices closer to $u$ than to $v$ is equal to the number of vertices closer to $v$ than to $u$. A graph $X$ is said to be {\it strongly…