A: Random Graph Generator

The function below generates a random graph (dot file) using Graphviz.

To render, ensure that graphviz is installed or save to file and render within documents using Quarto or similar.

import graphviz
import random
import string
from collections import defaultdict

def generate_random_graph(num_nodes=50, num_edges=100, num_clusters=5, colors=None):
    """Generates a random Graphviz graph with clusters and random colours.

    Args:
        num_nodes: Number of nodes in the graph.
        num_edges: Number of edges in the graph.
        num_clusters: Number of clusters to create.
        colors: List of colours to use for clusters (optional). If not provided, random colours will be used.
    """

    dot = graphviz.Digraph("G")
    dot.attr(fontname="Helvetica,Arial,sans-serif")
    dot.attr(layout="neato")
    dot.attr(start="random")
    dot.attr(overlap="false")
    dot.attr(splines="true")
    dot.attr(size="8,8")
    #dot.attr(dpi="300")

    # nodes to clusters, random colours if not provided
    cluster_assignments = {}
    if colors is None:
        colors = ["#%06x" % random.randint(0, 0xFFFFFF) for _ in range(num_clusters)] 

    for i in range(num_nodes):
        cluster_assignments[i] = random.randint(0, num_clusters - 1)

    # random node names, colouur assignment
    nodes = []
    for i in range(num_nodes):
        node_name = ''.join(random.choices(string.ascii_lowercase + string.digits, k=8))
        nodes.append(node_name)
        cluster_id = cluster_assignments[i]
        color = colors[cluster_id]
        dot.node(node_name, label="", shape="circle", height="0.12", width="0.12", fontsize="1", fillcolor=color, style="filled")
        

    # random edges (with a higher probability of staying within clusters)
    edges = []
    for _ in range(num_edges):
        src_cluster = random.randint(0, num_clusters - 1)
        dst_cluster = src_cluster if random.random() < 0.8 else random.randint(0, num_clusters - 1)  # 80% chance of staying in cluster
        src_node = random.choice([node for i, node in enumerate(nodes) if cluster_assignments[i] == src_cluster])
        dst_node = random.choice([node for i, node in enumerate(nodes) if cluster_assignments[i] == dst_cluster])
        edges.append((src_node, dst_node))

    #  edges to the graph
    for edge in edges:
        dot.edge(*edge)

    return dot