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).
This research output has an Altmetric Attention Score of 11. 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 30 April 2023.
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#4,574,177
of 34,567,073 outputs
Outputs from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#1,026
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Outputs of similar age
#46,560
of 311,826 outputs
Outputs of similar age from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#19
of 406 outputs
Altmetric has tracked 34,567,073 research outputs across all sources so far. Compared to these this one has done well and is in the 86th percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 24,740 research outputs from this source. They receive a mean Attention Score of 3.2. This one has done particularly well, scoring higher than 95% 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 311,826 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 84% of its contemporaries.
We're also able to compare this research output to 406 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 95% of its contemporaries.
