Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 41, Issue 38, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8113/41/38/385003
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Funding
- European Community [01194, FIS2004-05422]
- Santa Fe Institute
- [FIS2004-0542]
- [IST-FET ECAGENTS]
- ICREA Funding Source: Custom
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We analytically explore the scaling properties of a general class of nested subgraphs in complex networks, which includes the K-core and the K-scaffold, among others. We name such a class of subgraphs K-nested subgraphs since they generate families of subgraphs such that ... SK+1(G) subset of S-K(G) subset of SK-1(G) .... Using the so-called configuration model it is shown that any family of nested subgraphs over a network with diverging second moment and finite first moment has infinite elements (i.e. lacking a percolation threshold). Moreover, for a scale-free network with the above properties, we show that any nested family of subgraphs is self-similar by looking at the degree distribution. Both numerical simulations and real data are analyzed and display good agreement with our theoretical predictions.
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