# [Networkit] Hyperbolic graph generator

Daniel N. R. da Silva danielnascramos at gmail.com
Thu Sep 22 04:22:18 CEST 2016

```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

[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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