Capability centrality: the next step from scale-free property

TL;DR

This paper introduces ksi-centrality, a new network centrality measure that effectively distinguishes real networks from random ones and relates to network connectivity and growth parameters.

Contribution

The paper proposes ksi-centrality as a novel centrality measure, demonstrating its effectiveness in characterizing real networks and linking it to network properties like algebraic connectivity.

Findings

ksi-centrality distribution is right-skewed in real networks

Normalized ksi-centrality relates to algebraic connectivity and Chegeer's value

Average normalized ksi-centrality correlates with the number of edges in Barabasi-Albert model

Abstract

In this article we present a new centrality measure called ksi-centrality. We show that ksi-centrality distinguishes real networks from random ones, similar to degree centrality: the ksi-centrality distribution is right-skewed for real networks and centered for random Erdos-Renyi networks, and has linear pattern with a heavy tail on a log plot. Furthermore, the ksi-centrality distribution is centered for models simulating real networks: Barabasi-Albert, Watts-Strogatz, and Boccaletti-Hwang-Latora. Thus, this centrality distribution is an additional and independent property with respect to scale-freeness. We also introduce a normalized version of ksi-centrality and show that it is related to algebraic connectivity and the Chegeer's value of a network. Moreover, the average value of this normalized centrality is in bijective correspondence with the relative number of edges that a new node connects to others in the Barabasi-Albert preferential attachment model, thus answering the question of how to choose the parameter $m$ to model a given real-world network.