def traverse_with_confidence(
    start_node_id: str,
    relation: str,
    min_confidence: float = 0.80,
) -> list[dict]:
    results = []
    for path in graph.find_paths(start=start_node_id, edge_type=relation):
        identity_edges = [e for e in path.edges if e["relation"] == "SAME_AS"]
        if not identity_edges:
            results.append({"path": path, "path_confidence": 1.0})
            continue

        worst_case = min(e["properties"]["match_probability"] for e in identity_edges)
        if worst_case >= min_confidence:
            results.append({"path": path, "path_confidence": worst_case})

    return sorted(results, key=lambda x: x["path_confidence"], reverse=True)