/**
 * Degree Distribution Metrics
 *
 * Compares degree distributions between sampled subgraphs and ground truth graphs.
 * Used to measure structural representativeness of sampling methods.
 */
/**
 * Compute degree distribution as a normalized histogram.
 *
 * @param degrees - Array of degree values
 * @returns Map from degree to probability (sum = 1)
 */
export declare const computeDegreeDistribution: (degrees: number[]) => Map<number, number>;
/**
 * Compute KL divergence between two distributions.
 *
 * KL(P || Q) = Σ P(x) * log(P(x) / Q(x))
 *
 * Uses Laplace smoothing to handle zero probabilities.
 *
 * @param p - True distribution (what we want to approximate)
 * @param q - Approximate distribution (what we sampled)
 * @param smoothing - Laplace smoothing constant (default: 1e-10)
 * @returns KL divergence (non-negative, 0 = identical distributions)
 */
export declare const klDivergence: (p: Map<number, number>, q: Map<number, number>, smoothing?: number) => number;
/**
 * Compute Jensen-Shannon divergence (symmetric version of KL).
 *
 * JS(P, Q) = 0.5 * KL(P || M) + 0.5 * KL(Q || M)
 * where M = 0.5 * (P + Q)
 *
 * @param p - First distribution
 * @param q - Second distribution
 * @returns JS divergence in [0, log(2)] ≈ [0, 0.693]
 */
export declare const jsDivergence: (p: Map<number, number>, q: Map<number, number>) => number;
/**
 * Compute Earth Mover's Distance (Wasserstein-1) for degree distributions.
 *
 * EMD measures the minimum "work" to transform one distribution into another.
 * For 1D distributions, this equals the integral of the absolute difference
 * between cumulative distribution functions.
 *
 * @param p - First distribution
 * @param q - Second distribution
 * @returns EMD (non-negative)
 */
export declare const earthMoversDistance: (p: Map<number, number>, q: Map<number, number>) => number;
/**
 * Degree distribution comparison metrics.
 */
export interface DegreeDistributionMetrics {
    /** KL divergence from ground truth to sampled */
    klDivergence: number;
    /** Jensen-Shannon divergence (symmetric) */
    jsDivergence: number;
    /** Earth Mover's Distance */
    emd: number;
    /** Mean degree of sampled */
    sampledMeanDegree: number;
    /** Mean degree of ground truth */
    groundTruthMeanDegree: number;
    /** Standard deviation of sampled degrees */
    sampledStdDegree: number;
    /** Standard deviation of ground truth degrees */
    groundTruthStdDegree: number;
    /** Max degree in sampled */
    sampledMaxDegree: number;
    /** Max degree in ground truth */
    groundTruthMaxDegree: number;
}
/**
 * Compute comprehensive degree distribution comparison metrics.
 *
 * @param sampledDegrees - Degree values from sampled subgraph
 * @param groundTruthDegrees - Degree values from ground truth graph
 * @returns Complete comparison metrics
 */
export declare const compareDegreeDistributions: (sampledDegrees: number[], groundTruthDegrees: number[]) => DegreeDistributionMetrics;
/**
 * Compute degree distribution from a graph's node degrees.
 *
 * @param nodeDegrees - Map from node ID to degree
 * @returns Normalized degree distribution
 */
export declare const degreeDistributionFromMap: (nodeDegrees: Map<string, number>) => Map<number, number>;
/**
 * Compute degree histogram bucket counts (for visualization).
 *
 * @param degrees - Array of degree values
 * @returns Map from bucket label to count
 */
export declare const computeDegreeHistogram: (degrees: number[]) => Map<string, number>;
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