import * as tf from '../backend/adapter';
import { SparseMatrix } from './sparse';
/**
 * For *k*-NN graphs the affinity matrix must be symmetrised
 * (`A = 0.5 * (A + Aᵀ)`) before calling this function.
 */
export declare function degree_vector(A: tf.Tensor2D): tf.Tensor1D;
/**
 *     L = I  −  D^{-1/2} · A · D^{-1/2}
 *
 * where
 *   • `A` is the affinity / adjacency matrix
 *   • `D` is the diagonal *degree* matrix with `D[i,i] = Σ_j A[i,j]`
 *
 * Isolated vertices (zero degree) are handled gracefully by treating
 * `D^{-1/2}` as **0** for the corresponding diagonal entry which leaves the
 * row & column of `L` equal to the identity matrix (no connections).
 */
export declare function normalised_laplacian(A: tf.Tensor2D): tf.Tensor2D;
export declare function normalised_laplacian(A: tf.Tensor2D, return_diag: true): {
    laplacian: tf.Tensor2D;
    sqrt_degrees: tf.Tensor1D;
};
interface MatrixFreeOperator {
    n: number;
    matvec: (vector: Float64Array) => Float64Array;
}
interface SparseNormalisedLaplacian {
    operator: MatrixFreeOperator;
    sqrt_degrees: Float64Array;
    degrees: Float64Array;
}
export declare function sparse_normalised_laplacian_operator(affinity: SparseMatrix): SparseNormalisedLaplacian;
export {};