rustworkx.hyperbolic_random_graph

hyperbolic_random_graph(pos, beta, r, /, seed=None)

Return a hyperbolic random undirected graph (also called hyperbolic geometric graph).

The usual hyperbolic random graph model connects pairs of nodes with probability

$$P[(u,v)\in E]=\frac{1}{1+\exp (\beta (d(u,v)-R)/2)},$$

a sigmoid function that decreases as the hyperbolic distance between nodes $u$ and $v$ increases. The hyperbolic distance is given by

$$d(u,v)=\text{arccosh}[x_0(u)x_0(v)-\sum _{j=1}^D{x}_j(u)x_j(v)],$$

where $D$ is the dimension of the hyperbolic space and $x_d(u)$ is the $d$ th-dimension coordinate of node $u$ in the hyperboloid model. The number of nodes and the dimension are inferred from the coordinates pos. The 0-dimension “time” coordinate is inferred from the others.

If beta is None, all pairs of nodes with a distance smaller than r are connected.

This algorithm has a time complexity of $O(n^2)$ for $n$ nodes.

Parameters:

• pos (list[list[float]]) – Hyperboloid coordinates of the nodes [[$x_1(1)$, …, $x_D(1)$], [$x_1(2)$, …, $x_D(2)$], …]. The “time” coordinate $x_0$ is inferred from the other coordinates.

• beta (float) – Sigmoid sharpness (nonnegative) of the connection probability.

• r (float) – Distance at which the connection probability is 0.5 for the probabilistic model. Threshold when beta is None.

• seed (int) – An optional seed to use for the random number generator.

Returns:

A PyGraph object

Return type:

PyGraph