A change of perspective in network centrality

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.

Interplay Between Hierarchy and Centrality in Complex Networks

“…They are assigned an edge trussness t e (e ij ) = 1. The set of associated isolated nodes are also removed V t 1 = {5, 6,7,8,9,10,11,22,23,24, 25} resulting in the 1-truss network G t 1 . The process continues by removing all edges that participate in two triangles and not three triangles are removed.…”

“…The vast majority of centrality measures can be classified as neighborhood-based, path-based or iterative refinementbased measures [6]. While these measures are usually linked to a single topological property of the network, recent works turn to multidimensional definitions [7]- [10], [38]- [40].…”

Reconciling contrasting views on economic complexity

“…In most situations, the eigenvector corresponding to the largest eigenvalue λ 1 carries the maximum amount of information 27 and it is thus taken as solution (although we will demonstrate the potential of combining more eigenvectors). In complex network jargon, X c and Y p are (eigen-)centrality metrics in the bipartite network of countries and products 19,28 .…”

“…Grounded on these considerations, we promote here an integrated measure of economic complexity, which exploits the neatness of the proposed framework. By employing the recently introduced framework to deal with multidimensional centrality 28 , we combine the two existing measures into unique centrality metrics unveiling the multidimensional complexity of countries and products. Either using W A or W B to develop the new integrated measure of complexity would lead to reliable and comparable results.…”

“…The rationale to compute the GENEPY index grounds on two key points: firstly, to interpret the symmetric squared matrix N as the mathematical description of the weighted topology of an undirected network 26 such that the countries are the nodes and the similarities between the export baskets are the links connecting themand, secondly, to interpret the eigenvectors of N as the (multidimensional) eigenvector centrality of the nodes in the network. Using this approach, the eigenvectors are combined into a unique metrics (the GENEPY one), following a statistically grounded framework where the same eigenvectors are obtained as the result of a least-squares estimation exercise 28 (Methods section, Eqs. (18)- (19); for more details we refer the reader to Sciarra et al 28 ).…”