/**
 * A vertex (node) in a directed graph, holding metadata and a list of connected edges.
 * @typeParam VMetadata - The type of metadata stored on vertices
 * @typeParam EMetadata - The type of metadata stored on edges
 */
export type Vertex<VMetadata = null, EMetadata = null> = {
    metadata: VMetadata;
    edges: Array<Edge<EMetadata, VMetadata>>;
};
/**
 * A directed edge connecting two vertices, with its own metadata.
 * @typeParam EMetadata - The type of metadata stored on edges
 * @typeParam VMetadata - The type of metadata stored on the connected vertices
 */
export type Edge<EMetadata = null, VMetadata = null> = {
    metadata: EMetadata;
    from: Vertex<VMetadata, EMetadata>;
    to: Vertex<VMetadata, EMetadata>;
};
/**
 * A directed graph data structure supporting vertex/edge management and graph traversal algorithms
 * including breadth-first search, reverse BFS, and shortest path computation.
 *
 * @typeParam VMetadata - The type of metadata stored on vertices
 * @typeParam EMetadata - The type of metadata stored on edges
 */
export declare class Graph<VMetadata = null, EMetadata = null> {
    private readonly vertices;
    constructor();
    /**
     * Serializes the graph to a JSON string for debugging.
     * @param metadataRepr - Optional function to transform metadata values before serialization
     * @returns A pretty-printed JSON string of the graph structure
     */
    dump(metadataRepr?: (metadata: VMetadata | EMetadata) => any): string;
    /**
     * Adds a new vertex to the graph, optionally connecting it to existing vertices via edges.
     * @param metadata - The metadata to attach to the new vertex
     * @param fromEdges - Edges pointing from existing vertices to this new vertex
     * @param toEdges - Edges pointing from this new vertex to existing vertices
     * @returns The newly created vertex
     */
    addVertex(metadata: VMetadata, fromEdges: Array<Omit<Edge<EMetadata, VMetadata>, 'to'>>, toEdges: Array<Omit<Edge<EMetadata, VMetadata>, 'from'>>): Vertex<VMetadata, EMetadata>;
    /**
     * Returns a generator that yields all vertices matching the predicate.
     * @param predicate - A function to test each vertex
     * @returns A generator of matching vertices
     */
    findVertex(predicate: (vertex: Vertex<VMetadata, EMetadata>) => boolean): Generator<Vertex<VMetadata, EMetadata>, null>;
    /**
     * Adds a directed edge between two existing vertices.
     * @param metadata - The metadata to attach to the edge
     * @param from - The source vertex
     * @param to - The destination vertex
     * @returns The newly created edge
     */
    addEdge(metadata: EMetadata, from: Vertex<VMetadata, EMetadata>, to: Vertex<VMetadata, EMetadata>): Edge<EMetadata, VMetadata>;
    /**
     * Performs a breadth-first traversal following outgoing edges from the starting vertex or vertices.
     * @param from - A starting vertex, or a predicate to select multiple starting vertices
     * @returns A generator yielding vertices in BFS order
     */
    breadthFirstSearch(from: Vertex<VMetadata, EMetadata> | ((vertex: Vertex<VMetadata, EMetadata>) => boolean)): Generator<Vertex<VMetadata, EMetadata>, null>;
    /**
     * Performs a reverse breadth-first traversal following incoming edges from the starting vertex or vertices.
     * @param to - A starting vertex, or a predicate to select multiple starting vertices
     * @returns A generator yielding vertices in reverse BFS order
     */
    reverseBreadthFirstSearch(to: Vertex<VMetadata, EMetadata> | ((vertex: Vertex<VMetadata, EMetadata>) => boolean)): Generator<Vertex<VMetadata, EMetadata>, null>;
    /**
     * Finds the shortest path (by edge count) between two vertices using BFS.
     * @param from - The starting vertex, or a predicate to select starting vertices
     * @param to - The target vertex, or a predicate to identify target vertices
     * @returns An array of edges forming the shortest path, or `null` if no path exists
     */
    shortestPath(from: Vertex<VMetadata, EMetadata> | ((vertex: Vertex<VMetadata, EMetadata>) => boolean), to: Vertex<VMetadata, EMetadata> | ((vertex: Vertex<VMetadata, EMetadata>) => boolean)): Array<Edge<EMetadata, VMetadata>> | null;
}