Various topologies for representing three dimensional protein structures have been advanced for purposes ranging from prediction of folding rates to ab initio structure prediction. Examples include relative contact order, Delaunay tessellations, and backbone torsion angle distributions. Here we introduce a new topology based on a novel means for operationalizing three dimensional proximities with respect to the underlying chain. The measure involves first interpreting a rank-based representation of the nearest neighbors of each residue as a permutation, then determining how perturbed this permutation is relative to an unfolded chain. We show that the resultant topology provides improved association with folding and unfolding rates determined for a set of two-state proteins under standardized conditions. Furthermore, unlike existing topologies, the proposed geometry exhibits fine scale structure with respect to sequence position along the chain, potentially providing insights into folding initiation and/or nucleation sites. Segal: A Novel Topology for Representing Protein Folds The protein folding problem, or problems (Dill et al. 2007), despite considerable recent headway,