Find large, dense subgraphs in the undirected FlyWire connectome graph. A subgraph with k nodes and m edges is a δ-quasi-clique if:

m ≥ δ × k × (k − 1) / 2

Input & Objective

You’ll receive an unweighted, undirected graph G = (V, E). Your goal: extract up to 12 large quasi-cliques, one for each density level:

δi = 1/2i, i = 0, 1, ..., 11

Each solution yields subgraph sizes k0...k11. The score is:

k0/20 + k1/21 + ... + k11/211 (higher weights for denser subgraphs).

Notes:

• Every δ_i-quasi-clique is also valid for δ_i+1. You can submit fewer than 12 subgraphs; we’ll infer the rest.
• In case of score ties, earlier submissions rank higher.

Submit a single CSV file with one line per quasi-clique (up to 12). Our verifier will automatically determine which density each subgraph satisfies. See the benchmark example below.

Prerequisites

Open to all. No prior knowledge of neuroscience is needed—just strong data processing and algorithm skills.

Data

• Download the FlyWire connectome graph here; the file contains sorted node pairs (edges); if (x, y) is in the list, (y, x) is also an edge
• Sample benchmark solution: here
• Python code to verify submissions and calculate scores: Colab notebook

Submissions

• Email your CSV to arie@princeton.edu
• Each row = comma-separated neuron IDs (one subgraph per row); no headers or other info
• You can submit fewer than 12 rows; we’ll extend the solution based on the observation above
• Please run the verifier before submitting to confirm your score and ki values - you may include them in the email for verification
• Kindly introduce yourself in your first email, tell us where you learned about the challenge, and whether we can list your name on the leaderboard
• There's no limit on submissions — we’ll score your best one before the deadline
• Winners receive a special trophy from the FlyWire team at Pricneton University, and an optional invitation to present (see past winner presentations: 1, 2, 3)

Additional Notes

• Leaderboard shows placements only; all scores and solutions will be published after the deadline
• Challenge updated on July 21, 2025, to allow a range of density values (vs. fixed ones)
• Deadline extended from July 31 to August 31. No further changes or extensions are expected.