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Centrality is one of the most studied concepts in social network analysis. There is a huge literature regarding centrality measures, as ways to identify the most relevant users in a social network. The challenge is to find measures that can…

Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…

In recent years, the problem of identifying the spreading ability and ranking social network users according to their influence has attracted a lot of attention; different approaches have been proposed for this purpose. Most of these…

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…

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…

The problem of assigning centrality values to nodes and edges in graphs has been widely investigated during last years. Recently, a novel measure of node centrality has been proposed, called k-path centrality index, which is based on the…

Most network studies rely on an observed network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics,…

Node centrality is one of the most important and widely used concepts in the study of complex networks. Here, we extend the paradigm of node centrality in financial and economic networks to consider the changes of node "importance" produced…

Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard…

We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including…

A new measure to assess the centrality of vertices in an undirected and connected graph is proposed. The proposed measure, L1 centrality, can adequately handle graphs with weights assigned to vertices and edges. The study provides tools for…

In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation…

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…

Many systems, ranging from biological and engineering systems to social systems, can be modeled as directed networks, with links representing directed interaction between two nodes. To assess the importance of a node in a directed network,…

Influential nodes play a critical role in boosting or curbing spreading phenomena in complex networks. Numerous centrality measures have been proposed for identifying and ranking the nodes according to their importance. Classical centrality…

Network centrality is a foundational concept for quantifying the importance of nodes within a network. Many traditional centrality measures--such as degree and betweenness centrality--are purely structural and often overlook the dynamics…

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…

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…

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…

In real world complex networks, the importance of a node depends on two important parameters: 1. characteristics of the node, and 2. the context of the given application. The current literature contains several centrality measures that have…