import { Node, Connection } from '../../../../../types/core';
import { GraphCharacteristics, LayoutAlgorithm, AdjacencyMap } from './types';
/**
 * Build outgoing adjacency map from connections
 */
export declare function buildOutgoingMap(nodes: Node[], connections: Connection[]): AdjacencyMap;
/**
 * Build incoming adjacency map from connections
 */
export declare function buildIncomingMap(nodes: Node[], connections: Connection[]): AdjacencyMap;
/**
 * Build bidirectional adjacency map (treats graph as undirected)
 */
export declare function buildBidirectionalMap(nodes: Node[], connections: Connection[]): AdjacencyMap;
/**
 * Detect cycles in directed graph using DFS coloring
 * Returns true if the graph contains at least one cycle
 */
export declare function detectCycles(nodes: Node[], outgoing: AdjacencyMap): boolean;
/**
 * Count connected components using union-find approach
 */
export declare function countConnectedComponents(nodes: Node[], bidirectional: AdjacencyMap): number;
/**
 * Check if the graph is a tree
 * A tree has exactly n-1 edges, no cycles, and is connected
 */
export declare function isTree(nodes: Node[], connections: Connection[], outgoing: AdjacencyMap, bidirectional: AdjacencyMap): boolean;
/**
 * Calculate graph density
 * density = edges / (nodes * (nodes - 1)) for directed graph
 */
export declare function calculateDensity(nodeCount: number, edgeCount: number): number;
/**
 * Calculate degree statistics
 */
export declare function calculateDegreeStats(nodes: Node[], outgoing: AdjacencyMap, incoming: AdjacencyMap): {
    maxDegree: number;
    avgDegree: number;
};
/**
 * Analyze graph characteristics for algorithm selection
 */
export declare function analyzeGraph(nodes: Node[], connections: Connection[]): GraphCharacteristics;
/**
 * Select optimal layout algorithm based on graph characteristics
 */
export declare function selectAlgorithm(characteristics: GraphCharacteristics): LayoutAlgorithm;