/**
 * v1.3.2 §9.2 — domain-agnostic directed-graph core.
 *
 * Shared by agent-manager (delegation graph built from `collaborators`/
 * `used_by`) and workflow-manager (stage graph built from `depends_on`).
 *
 * Cycle detection is Kahn's algorithm (topological peel, O(V+E)) to find the
 * set of nodes that participate in *some* cycle; a bounded DFS over that
 * subgraph then recovers concrete node paths so callers can report
 * "a → b → a" rather than a bare "a cycle exists".
 */
export interface GraphNode {
    id: string;
}
export interface GraphEdge {
    from: string;
    to: string;
    /** Provenance label for diagnostics (which field declared the edge). */
    field?: string;
}
/**
 * Return every distinct simple cycle as an ordered node-id path with the
 * entry node repeated at the end (e.g. `["a","b","a"]`). A self-loop `a→a`
 * comes back as `["a","a"]`. Empty result ⇒ the graph is a DAG.
 */
export declare function detectCycles(nodes: GraphNode[], edges: GraphEdge[]): string[][];
/** Node ids reachable from none of `roots` (orphans). */
export declare function findUnreachable(roots: string[], nodes: GraphNode[], edges: GraphEdge[]): string[];
/**
 * Longest path length (in edges) reachable from `roots`. Returns `Infinity`
 * if a cycle is reachable — callers should run {@link detectCycles} first and
 * only trust this on a DAG. Used for the delegation depth cap.
 */
export declare function maxDepth(roots: string[], nodes: GraphNode[], edges: GraphEdge[]): number;