Central loops in random planar graphs

Abstract : Random planar graphs appear in a variety of context and it is important for many different applications to be able to characterize their structure. Local quantities fail to give interesting information and it seems that path-related measures are able to convey relevant information about the organization of these structures. In particular, nodes with a large betweenness centrality (BC) display non-trivial patterns, such as central loops. We first discuss empirical results for different random planar graphs and we then propose a toy model which allows us to discuss the condition for the emergence of non-trivial patterns such as central loops. This toy model is made of a star network with $N_b$ branches of size $n$ and links of weight $1$, superimposed to a loop at distance $\ell$ from the center and with links of weight $w$. We estimate for this model the BC at the center and on the loop and we show that the loop can be more central than the origin if $w
Type de document :
Pré-publication, Document de travail
t17/060. Revised and augmented version, 13 pages, 12 figures. 2017
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https://hal-cea.archives-ouvertes.fr/cea-01502150
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Soumis le : mercredi 5 avril 2017 - 10:25:49
Dernière modification le : jeudi 15 mars 2018 - 15:03:50
Document(s) archivé(s) le : jeudi 6 juillet 2017 - 13:08:55

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1611.03232.pdf
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  • HAL Id : cea-01502150, version 1
  • ARXIV : 1611.03232

Citation

Benjamin Lion, Marc Barthelemy. Central loops in random planar graphs. t17/060. Revised and augmented version, 13 pages, 12 figures. 2017. 〈cea-01502150〉

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