Add random graph generator (#5240)

* added complete graph generator function

* added doctest, type hints, wikipedia explanation

* added return type hint for function complete_graph

* added descriptive name for the parameter: n

* random graph generator with doctest and type hints

* validated using pre-commit

* Delete complete_graph_generator.py

* fixed doctest

* updated following reviews

* simplified the code following reviews

* fixed doctest and solved consistency issues

* consistency fixes

graphs/random_graph_generator.py

@@ -0,0 +1,67 @@
+"""
+* 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], 1: [0, 2, 3], 2: [1, 3], 3: [1, 2]}
+    >>> random.seed(1)
+    >>> random_graph(4, 0.5, True)
+    {0: [1], 1: [2, 3], 2: [3], 3: []}
+    """
+    graph = {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:
+    >>> print(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()