Related papers: An $\alpha$-triangle eigenvector centrality of gra…

Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problems of distributed estimation and control of…

Graph Convolutional Networks (GCNs) have achieved impressive performance in a wide variety of areas, attracting considerable attention. The core step of GCNs is the information-passing framework that considers all information from neighbors…

There are several applications that benefit from a definition of centrality which is applicable to sets of vertices, rather than individual vertices. However, existing definitions might not be able to help us in answering several network…

Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…

Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best…

We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex. Three distinct types of…

Semantic networks qualify the meaning of an edge relating any two vertices. Determining which vertices are most "central" in a semantic network is difficult because one relationship type may be deemed subjectively more important than…

This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…

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…

In the study of the behavior of centrality measures with respect to network modifications, score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc…

We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures. In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other…

Centrality indices are used to rank the nodes of a graph by importance: this is a common need in many concrete situations (social networks, citation networks, web graphs, for instance) and it was discussed many times in sociology,…

Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such…

In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…

Extracting information from real-world large networks is a key challenge nowadays. For instance, computing a node centrality may become unfeasible depending on the intended centrality due to its computational cost. One solution is 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…

Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…

This paper introduces a novel framework that combines traditional centrality measures with eigenvalue spectra and diffusion processes for a more comprehensive analysis of complex networks. While centrality measures such as degree,…

There are different measures to classify a network's data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological…