The cofactor of R[S] equals (-2)^{|S|-1} κ_G(S)/τ(G), and the normalized det R[S]/cof R[S] equals (2/|S|) tr Q + (1/2) q^T K q after Kron reduction, equivalently the max of u^T R[S] u for sum-u=1 vectors.
Devriendt,Effective resistance is more than distance: Laplacians, Simplices and the Schur complement, Linear Algebra and its Applications, 639 (2022), pp
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Generalizes finite-sample bounds for convex clustering from specific to general connected affinity graphs via random walks, yielding new convergence rates and emphasizing affinity weight tuning.
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Affinity Graph Connectivity in Convex Clustering
Generalizes finite-sample bounds for convex clustering from specific to general connected affinity graphs via random walks, yielding new convergence rates and emphasizing affinity weight tuning.