I need to generate an adjacency list for a random directed graph with a number of nodes n and a number of edges m. I have found this question, which is similar, but the edges exist or not based on probability.

CodePudding user response：

You can use a similar algorithm as in @kaya3's answer on the question you linked to. Instead of taking a probability p, take the number of edges m, and instead of iterating all possible edges, take a sample of it of size m. Make those edges unconditionally.

The original code allowed loops to be generated (a node having an edge to itself) when directed. As you briefly commented you didn't want to have such loops, I added the corresponding if condition:

from random import sample
from itertools import product, combinations

def random_graph(n, m, *, directed=False):
    nodes = range(n)
    adj_list = [[] for i in nodes]
    possible_edges = product(nodes, repeat=2) if directed else combinations(nodes, 2)
    for u, v in sample(list(possible_edges), m):
        if u != v:  # added
            adj_list[u].append(v)
            if not directed:
                adj_list[v].append(u)
    return adj_list