import { TestEdge, TestNode } from '../generation/generators/types';
/**
 * Check if graph is connected using BFS.
 * @param nodes
 * @param edges
 * @param directed
 */
export declare const isConnected: (nodes: TestNode[], edges: TestEdge[], directed: boolean) => boolean;
/**
 * Build adjacency list from edges.
 * @param nodes
 * @param edges
 * @param directed
 */
export declare const buildAdjacencyList: (nodes: TestNode[], edges: TestEdge[], directed: boolean) => Map<string, string[]>;
/**
 * Find connected components for density calculation.
 * Returns array of components, where each component is an array of node IDs.
 * @param nodes
 * @param edges
 * @param directed
 */
export declare const findComponentsForDensity: (nodes: TestNode[], edges: TestEdge[], directed: boolean) => string[][];
/**
 * Check if a graph is bipartite using BFS 2-coloring.
 * A graph is bipartite if and only if it is 2-colorable.
 * @param nodes
 * @param edges
 * @param directed
 */
export declare const checkBipartiteWithBFS: (nodes: TestNode[], edges: TestEdge[], directed: boolean) => boolean;
/**
 * Generate all k-combinations from array.
 * @param arr
 * @param array
 * @param k
 */
export declare const getCombinations: <T>(array: T[], k: number) => T[][];
/**
 * Check if 4 vertices form induced P4 (path on 4 vertices).
 * @param vertices
 * @param adjacency
 * @param directed
 */
export declare const hasInducedP4: (vertices: string[], adjacency: Map<string, Set<string>>, directed: boolean) => boolean;
/**
 * Find all induced cycles of given length.
 * @param vertices
 * @param adjacency
 * @param length
 * @param directed
 */
export declare const findInducedCycles: (vertices: string[], adjacency: Map<string, Set<string>>, length: number, directed: boolean) => string[][];
/**
 * Check if cycle has a chord (edge between non-consecutive vertices).
 * Cycle format: [v0, v1, ..., vn-1] where vertices form a cycle v0-v1-...-vn-1-v0.
 * @param cycle
 * @param adjacency
 * @param directed
 */
export declare const hasChord: (cycle: string[], adjacency: Map<string, Set<string>>, directed: boolean) => boolean;
/**
 * Check if graph is transitively orientable (simplified check).
 * @param nodes
 * @param edges
 * @param directed
 */
export declare const checkTransitiveOrientation: (nodes: TestNode[], edges: TestEdge[], directed: boolean) => boolean;
/**
 * Compute spectral radius approximation using power iteration.
 * Returns the largest eigenvalue (in absolute value) of the adjacency matrix.
 * @param nodes - Graph nodes
 * @param adjacency - Adjacency list
 * @returns Approximate spectral radius
 */
export declare const computeSpectralRadiusApproximation: (nodes: TestNode[], adjacency: Map<string, string[]>) => number;
/**
 * Compute algebraic connectivity (Fiedler value) using bounds.
 * Returns approximation of λ₂ (second smallest Laplacian eigenvalue).
 * Uses Fiedler value bounds for efficiency.
 * @param nodes - Graph nodes
 * @param adjacency - Adjacency list
 * @returns Approximate algebraic connectivity
 */
export declare const computeAlgebraicConnectivityBounds: (nodes: TestNode[], adjacency: Map<string, string[]>) => number;
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