min_cost_max_flow

Generic Description

Maximize flow while minimizing total cost.

Simple example:

CALL nexyron.min_cost_max_flow({source: 0, sink: 1})

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 min_cost_max_flow when maximize flow while minimizing total cost 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

min_cost_max_flow 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 max_flow by caring not only about quantity moved but also the price of moving it

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 max_flow by caring not only about quantity moved but also the price of moving it.

Advanced Example

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

CALL nexyron.min_cost_max_flow({source: 0, sink: 1}) YIELD source, target, flow, cost, max_flow
RETURN source, target, flow, cost, max_flow
LIMIT 10

Real Use Cases

Real Limitations And Tradeoffs