SageMath MCP Server

Graph Operation

graph_operation

Idempotent

Create named graphs or adjacency dicts and compute graph properties including chromatic number, connectivity, planarity, diameter, degree sequence, adjacency matrix, and shortest paths.

Instructions

Graph theory: create named graphs and compute properties (chromatic_number, is_connected, diameter, etc.)

Input Schema

TableJSON Schema

Name	Required	Description	Default
`graph`	Yes	Graph constructor: a named graph like 'PetersenGraph' or an adjacency dict like '{0:[1,2], 1:[0,2], 2:[0,1]}'
`source`	No	Source vertex
`target`	No	Target vertex
`session`	No	Workspace to use, as a name or a portable handle. Workspaces have independent variables. A name is scoped to this MCP session; a handle returned by start_sage_session (workspace_token) reaches the same workspace across reconnects and is a bearer credential -- keep it secret. Omit for 'default'.	default
`operation`	Yes	One of: chromatic_number, is_connected, is_planar, diameter, order, size, degree_sequence, adjacency_matrix, shortest_path (requires source and target)

Output Schema

TableJSON Schema

Name	Required	Description	Default
No arguments

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedv0.7.0Sep 12, 2026

changedInput schema / properties / session / description

Previous value: -"Named workspace to use. Workspaces have independent variables; omit for 'default'."New value: +"Workspace to use, as a name or a portable handle. Workspaces have independent variables. A name is scoped to this MCP session; a handle returned by start_sage_session (workspace_token) reaches the same workspace across reconnects and is a bearer credential -- keep it secret. Omit for 'default'."

Changed3 schema fields changedv0.5.0Aug 14, 2026

addedInput schema / properties / session

Added value: +{
+  "default": "default",
+  "description": "Named workspace to use. Workspaces have independent variables; omit for 'default'.",
+  "type": "string"
+}

changedInput schema / properties / source / anyOf

Previous value: -[
-  {
-    "type": "integer"
-  },
-  {
-    "type": "null"
-  }
-]New value: +[
+  {
+    "type": "integer"
+  },
+  {
+    "type": "string"
+  },
+  {
+    "type": "null"
+  }
+]

changedInput schema / properties / target / anyOf

Previous value: -[
-  {
-    "type": "integer"
-  },
-  {
-    "type": "null"
-  }
-]New value: +[
+  {
+    "type": "integer"
+  },
+  {
+    "type": "string"
+  },
+  {
+    "type": "null"
+  }
+]

First observedv0.3.1Jul 31, 2026

TDQS

B3.4/5.0

Behavior3/5

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

Annotations already carry idempotentHint=true and destructiveHint=false; the description adds that graphs can be constructed/named and properties computed. It does not say whether named graphs persist in a session or what happens on repeat creation, but the annotations cover most of the safety profile.

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 definition is one short, front-loaded sentence with a parenthetical list of operations and no filler. Every word contributes to scoping the tool.

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?

Given a rich schema, output schema, and annotations, the description is nearly sufficient: it names the domain and the action. It only lacks usage-selection context and side-effect detail, which are captured in other dimensions.

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?

Schema description coverage is 100%, so the schema fully documents graph, source, target, session, and operation. The description merely restates the operation domain and does not need to add parameter-level meaning.

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

Purpose4/5

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

The description anchors the tool with 'Graph theory' and names concrete actions ('create named graphs and compute properties') plus example operations, so an agent can tell it handles graph objects. It does not explicitly contrast with sibling tools such as group_operation or matrix_operation, which keeps it from a 5.

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?

There is no guidance on when to choose this tool over the many math siblings; it relies entirely on the 'Graph theory' prefix to imply applicability. No exclusions or alternative tool mentions are present.

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