Topological Sparsification of Protein Contact Networks via the Inverse Spielman-Srivastava Sieve: Evaluating Cycle-Space Leverage Scores against Local Graph Baselines and Structural Ground Truth

Protein domain organization and the identification of flexible hinge regions are important problems in structural biology and computational biophysics. Protein contact networks provide a framework for studying these properties, although conventional graph sparsification methods may remove interactions that contribute to the connectivity of protein cores. We present the Inverse Spielman–Srivastava Sieve, a graph sparsification method based on the cycle space of protein contact networks. The method projects network interactions onto the cycle space to distinguish edges participating in closed cycles from low-cycle connections, providing an alternative to cut-based sparsification approaches. We evaluate the method on 26 crystallographically verified protein structures and compare its performance with local triangle-counting and degree-based approaches, using structural domain assignments as a reference. For adenylate kinase, the method achieves a normalized mutual information (NMI) of 0.6456, compared with 0.0092 for the triangle-based baseline at the reported edge-retention settings. For calmodulin, it achieves NMI = 1.0000 over the reported retention range of 0.40–0.60. The analysis also examines the relationship between cycle-based network measures, protein domain organization, and potential hinge regions. The method provides a framework for studying protein contact network sparsification, structural domain decomposition, and candidate hinge regions using cycle-space projections.