Cyclic Edge Connectivity

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

With no annotations, the description carries the burden of explaining behavior, and it does disclose the key result semantics: the returned value is the smallest k when the cyclic edge connectivity falls in range, and null otherwise. It does not mention exhaustive-search performance limits or max_order behavior, though those are captured in the schema.

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

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

Two compact sentences: the first states the core computation, and the second explains interpretation and the next action. There is no filler, and the most important semantic information is front-loaded.

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

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

For a four-parameter computational tool with an output schema, the description covers the essential selection and interpretation workflow. It is not fully complete because it does not explicitly relate the tool to the sibling has_cyclic_edge_cut or explain the max_order exhaustive-search ceiling, but an agent can still invoke it correctly.

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

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

Schema coverage is 100%, so the baseline is 3, but the description adds meaning beyond the schema by explaining how kmin and kmax bound the search for the minimum cyclic k-edge-cut and how a null result should drive kmax adjustment. The graph and max_order parameters are already well documented in the schema.

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

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

The description defines the operation precisely: find the smallest k in the search range for which a cyclic k-edge-cut exists, and equate that with the cyclic edge connectivity. This distinguishes it from the sibling has_cyclic_edge_cut, which likely tests existence rather than computing the minimum.

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

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

The description gives useful post-invocation guidance: a null answer means no cut was found and kmax should be raised. However, it does not explicitly say when to choose this tool over alternatives such as has_cyclic_edge_cut or is_efec, so some selection context is left to inference.

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