#### Random Graph Generator

p
```"""
* Author: Manuel Di Lullo (https://github.com/manueldilullo)
* Description: Random graphs generator.
Uses graphs represented with an adjacency list.

URL: https://en.wikipedia.org/wiki/Random_graph
"""

import random

def random_graph(
vertices_number: int, probability: float, directed: bool = False
) -> dict:
"""
Generate a random graph
@input: vertices_number (number of vertices),
probability (probability that a generic edge (u,v) exists),
directed (if True: graph will be a directed graph,
otherwise it will be an undirected graph)
@examples:
>>> random.seed(1)
>>> random_graph(4, 0.5)
{0: , 1: [0, 2, 3], 2: [1, 3], 3: [1, 2]}
>>> random.seed(1)
>>> random_graph(4, 0.5, True)
{0: , 1: [2, 3], 2: , 3: []}
"""
graph: dict = {i: [] for i in range(vertices_number)}

# if probability is greater or equal than 1, then generate a complete graph
if probability >= 1:
return complete_graph(vertices_number)
# if probability is lower or equal than 0, then return a graph without edges
if probability <= 0:
return graph

# for each couple of nodes, add an edge from u to v
# if the number randomly generated is greater than probability probability
for i in range(vertices_number):
for j in range(i + 1, vertices_number):
if random.random() < probability:
graph[i].append(j)
if not directed:
# if the graph is undirected, add an edge in from j to i, either
graph[j].append(i)
return graph

def complete_graph(vertices_number: int) -> dict:
"""
Generate a complete graph with vertices_number vertices.
@input: vertices_number (number of vertices),
directed (False if the graph is undirected, True otherwise)
@example:
>>> complete_graph(3)
{0: [1, 2], 1: [0, 2], 2: [0, 1]}
"""
return {
i: [j for j in range(vertices_number) if i != j] for i in range(vertices_number)
}

if __name__ == "__main__":
import doctest

doctest.testmod()
```  