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amichae2

Math MCP Server

by amichae2

max_flow

Find the maximum possible flow from a source to a sink in a directed graph, given edge capacities.

Instructions

Compute maximum flow in a capacitated directed graph.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
edgesYes
sourceYes
sinkYes
capacitiesYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations provided, and the description lacks behavioral details such as complexity, graph constraints (e.g., acyclicity), or handling of infeasible flows. It does not disclose what happens when no path exists.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is a single sentence, very concise, and front-loaded. However, it could be slightly expanded to cover key details without losing conciseness.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given 4 required parameters with no schema descriptions and no annotations, the description is insufficient. It does not provide enough context for correct invocation, relying on the user's domain knowledge.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, but the description does not explain any of the 4 parameters. It only mentions 'capacitated directed graph' without detailing the format of edges, source, sink, or capacities.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool computes maximum flow in a capacitated directed graph, using specific verb and resource. It differentiates from sibling graph tools like shortest_path or spanning_tree.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance on when to use this tool vs alternatives, no prerequisites or exclusions mentioned. The description only states the basic operation.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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