calculate_laplacian

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

With no annotations, the description carries the full behavioral burden, and it delivers: it discloses ascending eigenvalue ordering, the meaning of the second eigenvalue (algebraic connectivity), that connection_type never mixes structural/functional/effective modalities, and that min_weight is not pre-applied when loading data. These are genuine operational traits beyond the schema, though it omits error behavior and output format details.

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 sentences with minimal filler; the core mathematical purpose is front-loaded and the parameter clarifications are compact. The algebraic-connectivity aside is mildly tangential but adds interpretive value without bloating the text.

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?

An output schema exists to handle return values, and the description covers the mathematical semantics of the tool plus two key parameters. However, atlas_id is unaddressed, no guidance distinguishes this tool from calculate_spectrum, and the absence of annotations leaves the safety/side-effect profile incomplete. For a medium-complexity tool this is adequate but has clear gaps.

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 description coverage is 0% and property titles are bare ('Atlas Id', 'Min Weight', 'Connection Type'), so the description must compensate. It adds real semantics for connection_type (never mixes modalities) and min_weight (explicit call-side threshold, not a data-loading filter), but leaves atlas_id unexplained.

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 identifies a specific artifact: the spectrum of the Laplacian of a real graph of an atlas, with precise mathematical characterization (eigenvalues ascending; second eigenvalue as algebraic connectivity). The verb and resource are clear, but it does not explicitly differentiate itself from the overlapping sibling calculate_spectrum.

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?

There is no guidance on when to use this tool versus alternatives such as calculate_spectrum, nor any prerequisites, exclusions, or conditions selecting this tool. The remark that min_weight 'decides who calls' hints at caller eligibility but operates only at parameter level and does not constitute tool-selection guidance.

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