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Hyperbolicity measures democracy in real-world networks

Overview of attention for article published in Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, September 2015
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About this Attention Score

  • Above-average Attention Score compared to outputs of the same age (63rd percentile)
  • High Attention Score compared to outputs of the same age and source (82nd percentile)

Mentioned by

twitter
7 tweeters

Citations

dimensions_citation
9 Dimensions

Readers on

mendeley
27 Mendeley
Title
Hyperbolicity measures democracy in real-world networks
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).

Twitter Demographics

The data shown below were collected from the profiles of 7 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 27 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Switzerland 2 7%
Italy 1 4%
United Kingdom 1 4%
Luxembourg 1 4%
Unknown 22 81%

Demographic breakdown

Readers by professional status Count As %
Researcher 7 26%
Professor 5 19%
Student > Master 4 15%
Student > Bachelor 3 11%
Student > Ph. D. Student 3 11%
Other 5 19%
Readers by discipline Count As %
Physics and Astronomy 8 30%
Computer Science 6 22%
Unspecified 4 15%
Mathematics 3 11%
Economics, Econometrics and Finance 2 7%
Other 4 15%

Attention Score in Context

This research output has an Altmetric Attention Score of 3. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 12 March 2015.
All research outputs
#6,317,794
of 12,351,064 outputs
Outputs from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#1,164
of 7,207 outputs
Outputs of similar age
#78,892
of 220,957 outputs
Outputs of similar age from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#47
of 276 outputs
Altmetric has tracked 12,351,064 research outputs across all sources so far. This one is in the 48th percentile – i.e., 48% of other outputs scored the same or lower than it.
So far Altmetric has tracked 7,207 research outputs from this source. They receive a mean Attention Score of 2.0. This one has done well, scoring higher than 84% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 220,957 tracked outputs that were published within six weeks on either side of this one in any source. This one has gotten more attention than average, scoring higher than 63% of its contemporaries.
We're also able to compare this research output to 276 others from the same source and published within six weeks on either side of this one. This one has done well, scoring higher than 82% of its contemporaries.