bellman_ford
Generic Description
Single-source shortest paths with negative-edge support and cycle detection.
Simple example:
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.
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