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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 different ways. In this paper, we examine a conjecture posed by E. Estrada regarding the ability of several measures to distinguish the vertices of networks. Estrada conjectured that if all vertices of a graph have the same subgraph centrality, then all vertices must also have the same degree, eigenvector, closeness, and betweenness centralities. We provide a counterexample for the latter two centrality measures and propose a revised conjecture.
Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of ep
We study network centrality based on dynamic influence propagation models in social networks. To illustrate our integrated mathematical-algorithmic approach for understanding the fundamental interplay between dynamic influence processes and static ne
Competition networks are formed via adversarial interactions between actors. The Dynamic Competition Hypothesis predicts that influential actors in competition networks should have a large number of common out-neighbors with many other nodes. We empi
There is an ever-increasing interest in investigating dynamics in time-varying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal ev
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures