cfpq_data.graphs.generators.labeled_binomial_graph

labeled_binomial_graph(n: int, p: float, *, labels: ~typing.List[str] = 'a', choice: ~typing.Callable[[~typing.List[str]], str] = <bound method Random.choice of <random.Random object>>, seed: int | None = None) → MultiDiGraph

Returns a \(G_{n,p}\) random graph, also known as an Erdős-Rényi graph or a binomial graph. With labeled edges.

The \(G_{n,p}\) model chooses each of the possible edges with probability \(p\).

Parameters:

nint

The number of nodes.

pfloat

Probability for edge creation.

labels: Iterable[str]

Labels that will be used to mark the edges of the graph.

choice: Callable[[Iterable[str]], str]

Function for marking edges.

seedinteger, random_state, or None (default)

Indicator of random number generation state.

Returns:

gMultiDiGraph

An Erdős-Rényi graph random graph.

Notes

This algorithm runs in \(O(n^2)\) time. For sparse graphs (that is, for small values of \(p\)), fast_labeled_binomial_graph() is faster.

References

[1]

16. Erdős and A. Rényi, On Random Graphs, Publ. Math. 6, 290 (1959).

[2]

5. 14. Gilbert, Random Graphs, Ann. Math. Stat., 30, 1141 (1959).

[3]

https://networkx.org/documentation/stable//reference/randomness.html#randomness

Examples

>>> from cfpq_data import *
>>> g = labeled_binomial_graph(42, 0.84, seed=42)
>>> g.number_of_nodes()
42
>>> g.number_of_edges()
1453