import type { CellComplex } from '../geometry/cell-complex.js';
import { MatN } from '../math/matn.js';
import { type SymmetricEigenOptions, type SymmetricEigensystem } from './symmetric-eigen.js';
export interface GraphLaplacianDiagnostics {
    readonly inputEdgeCount: number;
    readonly uniqueEdgeCount: number;
    readonly duplicateEdgeCount: number;
}
/** The unweighted combinatorial Laplacian of a CellComplex 1-skeleton. */
export interface GraphLaplacianOperator {
    readonly vertexCount: number;
    /** Canonical undirected pairs [minVertex, maxVertex], sorted lexicographically. */
    readonly edges: Uint32Array;
    readonly degrees: Uint32Array;
    /** Canonical connected-component IDs, ordered by each component's first vertex. */
    readonly componentOfVertex: Uint32Array;
    readonly componentCount: number;
    readonly diagnostics: GraphLaplacianDiagnostics;
    /** Applies Lx in O(V + E), supporting out === values. */
    apply(values: ArrayLike<number>, out?: Float64Array): Float64Array;
    /** Materializes the exact-integer Float64 reference matrix D - A. */
    toDense(): MatN;
}
export interface EigenvalueCluster {
    readonly start: number;
    readonly multiplicity: number;
    readonly value: number;
    readonly minimum: number;
    readonly maximum: number;
}
export interface GraphLaplacianModesOptions extends SymmetricEigenOptions {
    /** Relative gap used to group adjacent numerical eigenvalues. */
    clusterTolerance?: number;
}
export interface GraphLaplacianModes {
    readonly operator: GraphLaplacianOperator;
    readonly eigensystem: SymmetricEigensystem;
    readonly clusters: readonly EigenvalueCluster[];
}
/**
 * Builds L = D - A from all 1-cell groups in a CellComplex.
 *
 * The 1-skeleton is interpreted as a simple undirected graph. Repeated and
 * reversed edges are deduplicated and reported; self-loops and non-edge
 * 1-cell arities are rejected because their Laplacian semantics are not
 * implicit in this contract.
 */
export declare function graphLaplacian(complex: CellComplex): GraphLaplacianOperator;
/** Computes the complete dense modal basis of a CellComplex 1-skeleton. */
export declare function graphLaplacianModes(complex: CellComplex, options?: GraphLaplacianModesOptions): GraphLaplacianModes;
/** Returns the basis-independent orthogonal projector for one mode cluster. */
export declare function eigenspaceProjector(eigensystem: SymmetricEigensystem, cluster: EigenvalueCluster): MatN;
//# sourceMappingURL=graph-laplacian.d.ts.map