Related papers: The Parameterized Complexity of Centrality Improve…
We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…
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…
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts for the maximal smallest degree of a subgraph containing a…
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…
Betweenness is a well-known centrality measure that ranks the nodes according to their participation in the shortest paths of a network. In several scenarios, having a high betweenness can have a positive impact on the node itself. Hence,…
The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we…
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
This work deals with the issue of assessing the influence of a node in the entire network and in the subnetwork to which it belongs as well, adapting the classical idea of vertex centrality. We provide a general definition of relative…
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…
We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…
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…
The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem…
Betweenness centrality, measured by the number of times a vertex occurs on all shortest paths of a graph, has been recognized as a key indicator for the importance of a vertex in the network. However, the betweenness of a vertex is often…
Recent decades have witnessed the tremendous development of network science, which indeed brings a new and insightful language to model real systems of different domains. Betweenness, a widely employed centrality in network science, is a…
A new metric for quantifying pairwise vertex connectivity in graphs is defined and an implementation presented. While general in nature, it features a combination of input features well-suited for social networks, including applicability to…
Bonacich centrality measures the number of attenuated paths between nodes in a network. We use this metric to study network structure, specifically, to rank nodes and find community structure of the network. To this end we extend the…