import { Graph } from '../graph/graph';
import { BiconnectedResult } from '../types/clustering-types';
import { Edge, Node } from '../types/graph';
/**
 * Find biconnected components using Tarjan's algorithm.
 *
 * A biconnected component is a maximal subgraph where removing any single node
 * still leaves the graph connected. Articulation points (cut vertices) are nodes
 * whose removal increases the number of connected components.
 *
 * Use Case: Identify critical papers (articulation points) that connect research communities
 * in citation networks. Removing these papers would fragment the network.
 *
 * Algorithm Steps:
 * 1. DFS traversal with discovery time tracking
 * 2. Calculate low-link values (earliest ancestor reachable via back edges)
 * 3. Detect articulation points: low[child] ≥ disc[v]
 * 4. Extract components by popping edge stack on backtrack
 * 5. Handle disconnected graphs (DFS from each unvisited node)
 * @template N - Node type
 * @template E - Edge type
 * @param graph - Undirected graph to analyze
 * @returns Result containing biconnected components and articulation points, or error
 * @example
 * ```typescript
 * const graph = new Graph<PaperNode, CitationEdge>(false); // undirected
 * // ... add nodes and edges ...
 *
 * const result = biconnectedComponents(graph);
 * if (result.ok) {
 *   console.log(`Found ${result.value.articulationPoints.size} articulation points`);
 *   console.log(`Found ${result.value.components.length} biconnected components`);
 *
 *   result.value.components.forEach(component => {
 *     console.log(`Component ${component.id}: ${component.size} nodes`);
 *     if (component.isBridge) {
 *       console.log('  -> Bridge component');
 *     }
 *   });
 * }
 * ```
 */
export declare const biconnectedComponents: <N extends Node, E extends Edge>(graph: Graph<N, E>) => BiconnectedResult<string>;
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