A change of perspective in network centrality
Carla Sciarra, Guido Chiarotti, Francesco Laio, Luca Ridolfi

TL;DR
This paper introduces a new theoretical perspective on network centrality based on the adjacency matrix, revealing limitations of standard metrics and proposing more informative multi-component measures.
Contribution
It presents a natural, matrix-based framework for defining and comparing centrality measures, and introduces advanced multi-component metrics for complex networks.
Findings
Standard centrality metrics perform inadequately on complex networks
The proposed framework allows natural derivation of various centrality measures
Multi-component centrality metrics outperform traditional ones
Abstract
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 centrality. Centrality is a measure of the importance of the nodes in a network and it plays a crucial role in a huge number of fields, ranging from sociology to engineering, and from biology to economics. Many metrics are available to evaluate centrality. However, centrality measures are generally based on ad hoc assumptions, and there is no commonly accepted way to compare the effectiveness and reliability of different metrics. Here we propose a new perspective where centrality definition arises naturally from the most basic feature of a network, its adjacency matrix. Following this perspective, different centrality measures naturally emerge, including the…
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