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

With no annotations, the description carries the full burden and does disclose the underlying check (edge count vs v*(v-1)/2) plus the payment model (5 free trial calls per signed wallet), which is genuinely useful. However, it omits how the vertex count v is derived given only an `edges` input, and says nothing about the return value or error behavior.

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?

The functional clause is front-loaded and efficient, and the pricing note is short. The emoji and trial-call marketing append adds mild noise but does not obscure the core meaning.

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 simple boolean predicate with no output schema and one parameter, the definition is adequate but leaves the input encoding of `edges` and the derivation of v unexplained, which matters for calling 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?

One parameter at 0% schema coverage, so the description must compensate. It partially does by describing the input as an 'edge list', but does not specify the string format, separator, or whether vertex count is inferred — leaving the lone parameter only loosely characterized.

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 states a specific verb and resource ('Checks whether an edge list is a complete graph'), which an agent can distinguish from sibling graph tools like x402-graph-edge-count or x402-is-bipartite. It does not explicitly name a sibling or contrast scope, but the purpose is unambiguous.

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 predicate versus related tools (e.g. x402-graph-edge-count, x402-graph-vertex-count) and no stated preconditions. For a simple check tool usage is implied, but nothing is made explicit.

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