PlanarBench: Evaluating LLM Spatial Reasoning via Planar Graph Drawing

PlanarBench tests whether LLMs can draw planar graphs as ASCII art given only an edge list -- a spatial reasoning task that resists memorization because edge order, edge orientation, and node labels are all permutable. We evaluate 91 models on the 199 simplest non-isomorphic connected planar graphs (2 - 7 vertices). Edge count is the dominant difficulty predictor ($r = -0.85$) -- a finding not reported in prior LLM graph benchmarks, which use only node count as the difficulty axis.