Function bfs_with_predecessors 

pub fn bfs_with_predecessors(
    conn: &Connection,
    seed_entity_ids: &[i64],
    namespace: &str,
    min_weight: f64,
    max_hops: u32,
    max_neighbors_per_hop: Option<usize>,
) -> Result<(EntityDepthMap, PredecessorMap), AppError>

BFS that also returns a predecessor map for path reconstruction.

Used by deep-research to reconstruct directed evidence chains from discovered entities back to their seeds.

Returns (entity_depth, predecessor) where:

• entity_depth: minimum depth of each reached entity (0 = seed).
• predecessor: the BFS tree edge that first reached each non-seed entity.

When max_neighbors_per_hop is Some(k), only the top-k unvisited neighbours by weight DESC are followed at each entity expansion.

Errors

Propagates AppError::Database (exit 10) on SQLite query failures.