Concerning Iterative Graph Normalization and Maximum Weight Independent Sets

The paper proves: (i) normalizable binary fixed points of Nh are exactly maximal independent sets; (ii) the Jacobian at a MIS has spectrum {0} ∪ {h′(0)/s_i} and spectral radius h′(0)/dens_G(S), yielding local attractivity when <1 and quadratic convergence when h′(0)=0; (iii) non-maximal independent sets are repulsive under h′≠0; and (iv) a rectangular basin-of-attraction criterion for N when dens_G(S)≥2. The candidate solution establishes the same three core results and the optional basin criterion with slightly different arguments (e.g., a block-triangular Jacobian derivation, and a perturbation-based repulsivity argument), but all conclusions match the paper’s statements.