Function hyperbolic_random_graph 

pub fn hyperbolic_random_graph<R: Rng>(
    n: usize,
    r: f64,
    alpha: f64,
    rng: &mut R,
) -> Result<Graph<usize, f64>>

Generate a hyperbolic random graph (HRG) in the Poincaré disk model.

n nodes are placed uniformly at random in a hyperbolic disk of radius r according to the quasi-uniform distribution with curvature parameter alpha (controls degree heterogeneity; alpha = 0.5 recovers the pure geometric model, higher values concentrate nodes near the boundary). Two nodes are connected if their hyperbolic distance is at most r.

The hyperbolic distance between nodes at (r₁, θ₁) and (r₂, θ₂) in polar-hyperbolic coordinates is:

d(u,v) = acosh(cosh(r₁)·cosh(r₂) − sinh(r₁)·sinh(r₂)·cos(θ₁−θ₂))

Arguments

• n – number of nodes
• r – disk radius; larger r gives sparser graphs
• alpha – radial density exponent (> 0; 0.5 ≤ α ≤ 1 for scale-free degree)
• rng – random-number generator

Reference

Krioukov et al., “Hyperbolic geometry of complex networks”, Phys. Rev. E, 82(3), 036106, 2010.