Title |
Hyperbolicity measures democracy in real-world networks
|
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Published in |
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, September 2015
|
DOI | 10.1103/physreve.92.032812 |
Pubmed ID | |
Authors |
Michele Borassi, Alessandro Chessa, Guido Caldarelli |
Abstract |
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). |
X Demographics
Geographical breakdown
Country | Count | As % |
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United Kingdom | 2 | 29% |
United States | 1 | 14% |
Norway | 1 | 14% |
Unknown | 3 | 43% |
Demographic breakdown
Type | Count | As % |
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Members of the public | 4 | 57% |
Scientists | 2 | 29% |
Science communicators (journalists, bloggers, editors) | 1 | 14% |
Mendeley readers
Geographical breakdown
Country | Count | As % |
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Switzerland | 2 | 6% |
United Kingdom | 1 | 3% |
Luxembourg | 1 | 3% |
Italy | 1 | 3% |
Unknown | 29 | 85% |
Demographic breakdown
Readers by professional status | Count | As % |
---|---|---|
Researcher | 8 | 24% |
Professor | 6 | 18% |
Student > Master | 5 | 15% |
Student > Ph. D. Student | 4 | 12% |
Student > Bachelor | 3 | 9% |
Other | 6 | 18% |
Unknown | 2 | 6% |
Readers by discipline | Count | As % |
---|---|---|
Computer Science | 9 | 26% |
Physics and Astronomy | 8 | 24% |
Mathematics | 3 | 9% |
Medicine and Dentistry | 3 | 9% |
Economics, Econometrics and Finance | 2 | 6% |
Other | 3 | 9% |
Unknown | 6 | 18% |