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Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as resilience, navigability and small distances. We introduce a variational principle to explain how vertices tend to cluster in triangles as a function of their degrees. We apply the variational principle to the hyperbolic model that quickly gains popularity as a model for scale-free networks with latent geometries and clustering. We show that clustering in the hyperbolic model is non-vanishing and self-averaging, so that a single random graph sample is a good representation in the large-network limit. We also demonstrate the variational principle for some classical random graphs including the preferential attachment model and the configuration model.
| Taal | Engels |
|---|---|
| Artikelnummer | 295101 |
| Aantal pagina's | 20 |
| Tijdschrift | Journal of Physics A: Mathematical and Theoretical |
| Volume | 52 |
| Nummer van het tijdschrift | 29 |
| DOI's | |
| Status | Gepubliceerd - 24 jun 2019 |
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Scale-free network clustering in hyperbolic and other random graphs. / Stegehuis, Clara (Corresponding author); van der Hofstad, Remco; van Leeuwaarden, Johan S.H.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 52, Nr. 29, 295101, 24.06.2019.Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review
TY - JOUR
T1 - Scale-free network clustering in hyperbolic and other random graphs
AU - Stegehuis,Clara
AU - van der Hofstad,Remco
AU - van Leeuwaarden,Johan S.H.
PY - 2019/6/24
Y1 - 2019/6/24
N2 - Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as resilience, navigability and small distances. We introduce a variational principle to explain how vertices tend to cluster in triangles as a function of their degrees. We apply the variational principle to the hyperbolic model that quickly gains popularity as a model for scale-free networks with latent geometries and clustering. We show that clustering in the hyperbolic model is non-vanishing and self-averaging, so that a single random graph sample is a good representation in the large-network limit. We also demonstrate the variational principle for some classical random graphs including the preferential attachment model and the configuration model.
AB - Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as resilience, navigability and small distances. We introduce a variational principle to explain how vertices tend to cluster in triangles as a function of their degrees. We apply the variational principle to the hyperbolic model that quickly gains popularity as a model for scale-free networks with latent geometries and clustering. We show that clustering in the hyperbolic model is non-vanishing and self-averaging, so that a single random graph sample is a good representation in the large-network limit. We also demonstrate the variational principle for some classical random graphs including the preferential attachment model and the configuration model.
KW - clustering
KW - Complex networks
KW - hyperbolic model
KW - random graphs
UR - http://www.scopus.com/inward/record.url?scp=85069529720&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ab2269
DO - 10.1088/1751-8121/ab2269
M3 - Article
VL - 52
JO - Journal of Physics A: Mathematical and Theoretical
T2 - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 29
M1 - 295101
ER -