---
title: prim
url: https://nexyron.tech/docs/cypher/procedures/algorithms/trees-and-flow/prim
description: Minimum spanning tree construction by growing from a frontier.
---

# prim

## Generic Description

Minimum spanning tree construction by growing from a frontier.

Simple example:

```cypher
CALL nexyron.prim()
```

Tree and flow procedures optimize connectivity or movement through weighted graphs. They are useful for network design, allocation, dependency coverage, and capacity analysis.

## Consumer-Level Explanation

Use `prim` when minimum spanning tree construction by growing from a frontier 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. These algorithms make stronger assumptions about weights, terminals, prizes, and capacities than simple traversal, so parameter meaning must be explicit.

## Conceptual Explanation

`prim` 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

Prim and Kruskal solve a similar goal but often behave differently operationally on the way there

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

Prim and Kruskal solve a similar goal but often behave differently operationally on the way there.

## Advanced Example

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

```cypher
CALL nexyron.prim() YIELD source, target, weight
RETURN source, target, weight
LIMIT 10
```

## Real Use Cases

-   incremental MST reasoning
-   weighted network skeletons
-   backbone extraction
-   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

-   same caveat: garbage-in edge weights create garbage-out trees
-   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