Generate Pareto Front

Pareto Front Generation link

The Pareto front lets you explore the trade-off between intra-community density (how tight each community is) and inter-community separation (how distinct communities are). Instead of a single “best” solution, you get a spectrum of optimal solutions—so you can pick the one that balances density and separation to your liking.

Instantiate the Algorithm link

First, set up HpMocd exactly as in the Basic Usage section:

  import networkx as nx
from pymocd import HpMocd

G = nx.karate_club_graph()
alg = HpMocd(
    graph=G,
    debug_level=1,
    pop_size=100,
    num_gens=100,
    cross_rate=0.8,
    mut_rate=0.2
)
  

Generate the Pareto Front link

Call the `generate_pareto_front() method:

  frontier = alg.generate_pareto_front()
  

• Return value: A list of tuples [(assignment, metrics), …]

  • assignment (dict[int, int]): maps each node → community ID

  • metrics (tuple[float, float]):

    • [0] = inter-community score
    • [1] = intra-community score

Inspect a Solution link

Suppose you want the solution at index 23:

  labels, (intra_score, inter_score) = frontier[23]

print("Node → Community:", labels)
print(f"Inter: {intra_score:.4f}, Intra: {inter_score:.4f}")
  

Selecting Your Preferred Solution link

Now that you have the full Pareto front, you can choose:

• Maximum intra-community density Pick the tuple with the highest intra_score.
• Minimum inter-community connectivity Pick the tuple with the lowest inter_score.
• Combined metric or domain-specific measure Compute modularity, conductance, cut ratio, etc., on each labels dict and choose the best.
• Manual or visual selection Plot (inter_score, intra_score) to see the frontier and pick by eye.

  # Example: find index of highest intra score
best_intra_idx = max(range(len(frontier)), key=lambda i: frontier[i][1][1])
best_labels, best_metrics = frontier[best_intra_idx]

print(best_labels)
print(best_metrics)