---
id: analysis/ordering
name: Implement execution ordering functions (topologicalOrder, parallelGroups, criticalPath, reachableFrom)
status: completed
depends_on:
  - graph/flowgraph-class
  - graph/queries
scope: narrow
risk: low
impact: component
level: implementation
---

## Description

Implement the standalone analysis functions for execution ordering. These are pure functions operating on FlowGraph instances, delegating to graphology-dag algorithms.

## Acceptance Criteria

- [ ] `topologicalOrder(graph: FlowGraph): string[]` — uses graphology-dag topologicalSort, throws CycleError on cycles
- [ ] `parallelGroups(graph: FlowGraph): string[][]` — groups by dependency depth (group 0 = roots, group 1 = dependents of group 0, etc.)
- [ ] `criticalPath(graph: FlowGraph): string[]` — longest path through DAG
- [ ] `reachableFrom(graph: FlowGraph, nodeIds: string[]): Set<string>` — BFS/DFS from starting nodes
- [ ] `ancestors(graph: FlowGraph, nodeId: string): string[]` and `descendants(graph: FlowGraph, nodeId: string): string[]`
- [ ] All functions are standalone (not FlowGraph methods), in `src/analysis/`
- [ ] O(V + E) complexity for all — documented in JSDoc
- [ ] Unit tests: known DAGs produce expected orderings, parallel groups, critical paths

## References

- docs/architecture/analysis.md — execution ordering functions, performance characteristics
- docs/architecture/flowgraph-api.md — convenience delegation from FlowGraph to standalone functions

## Notes

> To be filled by implementation agent

## Summary

> To be filled on completion