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.
From: Mikhail Tuzhilin [view email]
[v1]
Tue, 5 May 2026 14:25:15 UTC (2,997 KB)
[v2]
Wed, 6 May 2026 08:55:34 UTC (2,997 KB)
[v3]
Thu, 7 May 2026 16:30:55 UTC (2,997 KB)
[v4]
Fri, 3 Jul 2026 11:49:24 UTC (3,760 KB)
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