/**
 * Path Diversity Metrics
 *
 * Measures how diverse a set of paths are from each other.
 * Higher diversity indicates the paths explore different regions of the graph.
 */
/**
 * Compute Jaccard distance between two sets.
 * Jaccard distance = 1 - Jaccard similarity = 1 - |A ∩ B| / |A ∪ B|
 *
 * @param setA - First set
 * @param setB - Second set
 * @returns Distance in [0, 1] where 0 = identical, 1 = completely disjoint
 */
export declare const jaccardDistance: <T>(setA: Set<T>, setB: Set<T>) => number;
/**
 * Convert a path (array of node IDs) to a set for Jaccard computation.
 *
 * @param path - Array of node IDs forming a path
 * @returns Set of node IDs
 */
export declare const pathToNodeSet: (path: string[]) => Set<string>;
/**
 * Compute mean pairwise Jaccard distance between paths.
 *
 * This measures how different the paths are from each other on average.
 * Higher values indicate more diverse path exploration.
 *
 * @param paths - Array of paths, where each path is an array of node IDs
 * @returns Mean pairwise Jaccard distance in [0, 1]
 */
export declare const meanPairwiseJaccardDistance: (paths: string[][]) => number;
/**
 * Compute path diversity using edge overlap.
 *
 * Converts paths to edge sets and computes Jaccard distance.
 * This is more sensitive than node-based diversity because
 * paths can share nodes but use different edges.
 *
 * @param paths - Array of paths, where each path is an array of node IDs
 * @returns Mean pairwise edge-based Jaccard distance in [0, 1]
 */
export declare const meanPairwiseEdgeJaccardDistance: (paths: string[][]) => number;
/**
 * Comprehensive path diversity metrics.
 */
export interface PathDiversityMetrics {
    /** Number of distinct paths */
    pathCount: number;
    /** Mean pairwise node-based Jaccard distance */
    nodeJaccardDistance: number;
    /** Mean pairwise edge-based Jaccard distance */
    edgeJaccardDistance: number;
    /** Total unique nodes across all paths */
    uniqueNodeCount: number;
    /** Total unique edges across all paths */
    uniqueEdgeCount: number;
    /** Average path length */
    meanPathLength: number;
    /** Standard deviation of path lengths */
    stdPathLength: number;
}
/**
 * Compute comprehensive path diversity metrics.
 *
 * @param paths - Array of paths, where each path is an array of node IDs
 * @returns Complete diversity metrics
 */
export declare const computePathDiversityMetrics: (paths: string[][]) => PathDiversityMetrics;
/**
 * Compute hub coverage: fraction of paths traversing high-degree nodes.
 *
 * @param paths - Array of paths, where each path is an array of node IDs
 * @param hubNodes - Set of node IDs considered "hubs" (high-degree nodes)
 * @returns Fraction of paths that traverse at least one hub
 */
export declare const computeHubCoverage: (paths: string[][], hubNodes: Set<string>) => number;
/**
 * Identify hub nodes (top percentile by degree).
 *
 * @param nodeDegrees - Map from node ID to degree
 * @param percentile - Top percentile to consider as hubs (e.g., 0.1 for top 10%)
 * @returns Set of hub node IDs
 */
export declare const identifyHubNodes: (nodeDegrees: Map<string, number>, percentile?: number) => Set<string>;
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