First Problem

This page runs one problem from nothing to a real answer. It does not explain how the pieces work – What Happened does that once you have seen a result to explain.

Max-Cut

Max-Cut splits a graph’s nodes into two groups to maximise the total weight of edges crossing between them. Quadratic Models derives its formulation by hand on a three-node graph; examples/maxcut/ is the same problem, runnable, on a graph you pick the size of.

Run It

With XQuad installed and the examples checked out, per Install XQuad:

$ uv run python examples/maxcut/runner.py --seed 42
{
  "_note": "canonical CI golden",
  "_seed": 42,
  "cut_weight": 354,
  "energy": -354,
  "n": 5,
  "partition": [
    0,
    1,
    0,
    0,
    1
  ],
  "valid": 1
}

No flags beyond --seed are required: --n defaults to 5, and --solver defaults to cpu, the baseline that needs no hardware or credentials.

Reading the Result

partition is the answer: one 0 or 1 per node, five nodes here, naming which side of the cut each node is on. cut_weight is the total weight of edges connecting a 0-side node to a 1-side node – the quantity Max-Cut maximises. energy is -354, the negative of cut_weight, because the model minimises -1 times the cut weight to turn maximising into the minimising every XQuad model does; see Quadratic Models for why that sign flip is exact. valid: 1 confirms every value in partition is 0 or 1 – the only thing this problem’s verifier checks, since Max-Cut declares no constraint beyond that.

Next: What Happened names each step this run took, in order, and links to where each one is covered in full.