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 measures the importance of the nodes in a network and it plays a crucial role in several fields, ranging from sociology to engineering, and from biology to economics. Many centrality metrics are available. However, these 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 degree, eigenvector, and hub-authority centrality. Within this theoretical framework, the effectiveness of different metrics is evaluated and compared. Tests on a large set of networks show that the standard centrality metrics perform unsatisfactorily, highlighting intrinsic limitations for describing the centrality of nodes in complex networks. More informative multi-component centrality metrics are proposed as the natural extension of standard metrics.
Highlights
Suppose a large number of individuals or entities interact in a network
Centrality becomes the node-property through which one estimates the adjacency matrix of the network, breaking new ground in the way we understand node centrality
Many of the most commonly used centrality metrics can be deduced within this theoretical framework, paving the way for an unprecedented chance to quantitatively compare the performances of different centrality measures
Summary
Suppose a large number of individuals or entities interact in a network. A long-standing challenge is to rank these individuals for their relevance in the system, i.e., for the centrality of the nodes or agents in a network science jargon. Recasting these centrality metrics into this new Undirected networks Estimator function f When considered under the perspective of the unique contribution, the expansion with s = N copies the same information of the node degree, in terms of the obtained nodes’ ranking.
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