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Hyperbolicity measures democracy in real-world networks

Borassi, Michele and Chessa, Alessandro and Caldarelli, Guido Hyperbolicity measures democracy in real-world networks. Physical Review E, 92 (3). 032812. ISSN 1539-3755 (2015)

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In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is “aristocratic”, since few elements “connect” the system, while a non-hyperbolic network has a more “democratic” structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an “influence area” for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define “local” networks (i.e., social or peer-to-peer networks), and large in “global” networks (i.e., power grid, metabolic networks, or autonomous system networks).

Item Type: Article
Identification Number: 10.1103/PhysRevE.92.032812
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HM Sociology
Q Science > QC Physics
Research Area: Economics and Institutional Change
Depositing User: Caterina Tangheroni
Date Deposited: 02 Nov 2015 13:32
Last Modified: 02 Nov 2015 13:32
URI: http://eprints.imtlucca.it/id/eprint/2792

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