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nikhilxnarula

sagemath-mcp

Identify Graph

identify_graph

Identify if a graph6 string or registry name corresponds to a known named graph in the registry, checking up to isomorphism.

Instructions

Is this graph one of the registry's named graphs, up to isomorphism?

Useful for a bare graph6 string that may be a relabelling of a well-known graph.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
graphYesa graph6 string or a registry name.

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

A4.2/5.0
Behavior4/5

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

With no annotations, the description carries the full burden of explaining behavior. It discloses the key behavioral trait: matching up to isomorphism rather than requiring exact string equality. It also indicates accepted input kinds (graph6 string or registry name). Return details are left to the output schema, which is acceptable.

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

Conciseness5/5

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

The description is two short sentences with no filler. The core purpose is front-loaded as a question, and the usage hint follows immediately. Every word earns its place.

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

Completeness4/5

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

For a single-parameter tool with an output schema, the description covers the core question, the isomorphism nuance, and the typical use case. It is complete enough for an agent to select and invoke the tool correctly, though it could optionally mention what kind of result is returned.

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

Parameters3/5

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

The input schema already fully describes the only parameter as 'a graph6 string or a registry name,' so schema coverage is 100%. The description adds context about relabelling and well-known graphs, but it does not materially expand the parameter semantics beyond the schema.

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 states a precise predicate: whether an input graph is one of the registry's named graphs up to isomorphism. This clearly distinguishes it from sibling tools like graph_info or analyze, which do generic graph analysis.

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

Usage Guidelines4/5

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

The description explicitly notes it is useful for a bare graph6 string that may be a relabelling of a well-known graph, giving clear context for when to invoke it. It does not explicitly mention alternatives or when not to use it, but the context is sufficient for a single-purpose tool.

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