---
title: bellman_ford
url: https://nexyron.tech/docs/cypher/procedures/algorithms/shortest-path-and-routing/bellman-ford
description: Single source shortest paths with negative edge support and cycle detection.
---

# bellman_ford

## Generic Description

Single-source shortest paths with negative-edge support and cycle detection.

Simple example:

```cypher
CALL nexyron.bellman_ford({source: 0})
```

Shortest-path and routing procedures compute feasible routes under different cost and graph assumptions. They are useful for logistics, dependency chains, impact paths, and path-based explainability.

## Consumer-Level Explanation

Use `bellman_ford` when single-source shortest paths with negative-edge support and cycle detection is the graph-analysis or operational question you actually need to answer. Keep the call explicit because its `YIELD` columns, row grain, and required runtime state determine how the rest of the Cypher pipeline can safely compose it.

## Conceptual Explanation

`bellman_ford` should be read as one named procedure contract in the broader Nexyron Cypher surface. The procedure call is not only a syntax hook: it defines what runtime state, projection, registry entry, or graph algorithm is being asked to operate, and it determines which output columns downstream `YIELD`, `WITH`, and `RETURN` stages can safely use.

## More Detailed Explanation

This differs from Dijkstra because it can handle negative edges and explicitly surface negative-cycle issues

In practical queries, start by deciding the row grain you want after the call: one row per node, one row per path, one row per registry object, one row per artifact, or one row per summary. Then keep that grain explicit with `YIELD` and named projections. That is the difference between a useful planner-facing example and a vague call that downstream tooling cannot safely compose. For contract-driven procedures, the executable examples on these pages intentionally inspect procedure metadata unless the required named artifacts are created in the same example.

## How It Differs From Nearby Algorithms

This differs from Dijkstra because it can handle negative edges and explicitly surface negative-cycle issues.

## Advanced Example

This example yields named columns from `bellman_ford` and returns a bounded result shape that downstream planner tooling can compose without guessing column names or row grain.

```cypher
CALL nexyron.bellman_ford({source: 0}) YIELD node_id, distance, has_negative_cycle
RETURN node_id, distance, has_negative_cycle
LIMIT 10
```

## Real Use Cases

-   financial or score-adjusted path analysis
-   graphs with penalty or rebate edges
-   validation of weighted graph assumptions
-   compare algorithm output with domain labels or time windows before operationalizing it
-   feed graph-analytic scores into ranked reports, feature contracts, or investigation queues only after checking the modeling assumptions

## Real Limitations And Tradeoffs

-   more expensive than Dijkstra on benign graphs
-   algorithm output reflects the projected graph, not an abstract real-world network outside the data model
-   nearby algorithms can answer different questions even when their output columns look similar