Hyperbolicity measures democracy in real-world networks
| Autor: | Michele Borassi, Guido Caldarelli, Alessandro Chessa |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
FOS: Computer and information sciences
real-world Physics - Physics and Society Theoretical computer science media_common.quotation_subject FOS: Physical sciences Physics and Society (physics.soc-ph) computer.software_genre 01 natural sciences 010305 fluids & plasmas Geometric networks Spatial network 0103 physical sciences Power grid 010306 general physics media_common Mathematics Social and Information Networks (cs.SI) Water transport Computer Science - Social and Information Networks complex networks Complex network Democracy Vertex (geometry) Settore FIS/02 - Fisica Teorica Modelli e Metodi Matematici Evolving networks Data mining computer |
| Zdroj: | Physical Review E Physical review. E, Statistical, nonlinear, and soft matter physics 92 (2015): 032812. doi:10.1103/PhysRevE.92.032812 info:cnr-pdr/source/autori:Michele Borassi (1); Alessandro Chessa (2); Guido Caldarelli (3)/titolo:Hyperbolicity measures democracy in real-world networks/doi:10.1103%2FPhysRevE.92.032812/rivista:Physical review. E, Statistical, nonlinear, and soft matter physics (Print)/anno:2015/pagina_da:032812/pagina_a:/intervallo_pagine:032812/volume:92 |
| ISSN: | 1539-3755 |
| DOI: | 10.1103/PhysRevE.92.032812 |
| Popis: | We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer networks. On the other hand, if the network is built in order to reach a "global" goal, as in metabolic networks or autonomous system networks, the influence area is much larger, and it can contain up to half the vertices in the graph. In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks. |
| Databáze: | OpenAIRE |
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