[Networkit] Hyperbolic graph generator

Henning Meyerhenke henning.meyerhenke at kit.edu
Thu Sep 22 09:03:35 CEST 2016

Dear Daniel,

Thank you very much for your interest and your feedback.

Moritz (cc) will be back from vacation on Monday. I am sure he will be
able to shed light on these issues and provide the necessary support via
the mailing list.

Best regards,

Am 22.09.16 um 04:22 schrieb Daniel N. R. da Silva:
> I'm interested in using the static Hyperbolic Random Geometric Graph
> Generator (HRGGG) - that's quite a name :) -
> (networkit.generators.HyperbolicGenerator) and got some doubts.
> I read [1] and according to its authors, HRGG have four parameters to be
> manipulated: number of nodes, ~average degree, ~power law exponent, and
> temperature. Looking for a generator, I found [2]. Their authors claim
> that the user can manipulate the four parameters using their proposed
> generator. But I realized after reading [3], that [2] takes too much
> time to generate large networks. So I went for [3]. But reading it, I
> realized that, roughly speaking, the temperature parameter is fixed at
> 0, not a function anymore, i.e, the generator uses a more specific
> model: the threshold random hyperbolic graphs one (unit-disk graphs in
> hyperbolic space). 
> So I got a little confused with the function docstring in NetworKit
> library: 
> HyperbolicGenerator(n, k=6, gamma=3, T=0) Parameters ---------- n :
> integer number of nodes k : double average degree gamma : double
> exponent of power-law degree distribution T : double temperature of
> statistical model
> My questions (using networkit generator):
> * T has a default value of 0, but I was able to manipulate it. Am I
> supposed to do this kind of manipulation? 
> * I did some preliminary tests using T > 0 and noted that the degree
> distribution got pretty weird, plotting it, it did not seem to be
> Poisson or Power Law. Also, I increased the power law exponent, and as I
> did it, the degree distribution started to look more like a Poisson
> distribution centered around the average degree. Concerning to the
> clustering coefficient, when I increased the Power Law exponent, the
> clustering decreased. Moreover, as T increased, the clustering
> coefficient substantially decreased. Are those things supposed to happen? 
> * [2] claims that when the power law exponent and the temperature
> approach inf, the hyperbolic graph degenerates to Erdos Renyi Random
> Graph Model. Does Networkit generator have the same properties/regimes
> presented on Table 1 ([2] pg. 2)?
> I know that it's a lot of questions and appreciate any help.
> Ps:
> * On NetworKit jupyter notebooks documentation page, only the "NetworKit
> User Guide" link is working.
> [1] Krioukov, et al. Hyperbolic Geometry of Complex Networks. 2010
> [2] Aldecoa, et al. Hyperbolic Graph Generator. 2015
> [3] Looz and Ozdayi. Generating massive complex networks with hyperbolic
> geometry faster in practice. 2016
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Karlsruhe Institute of Technology (KIT)
Institute of Theoretical Informatics (ITI)

Prof. Dr. Henning Meyerhenke
Theoret. Informatics / Parallel Computing

Phone: +49-721-608-41876
Web: http://parco.iti.kit.edu/henningm/

KIT - The Research University in the Helmholtz Association

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