Graph Modeler Skill

Purpose

Convert problem descriptions into appropriate graph representations, identifying entities as nodes and relationships as edges.

Capabilities

• Entity-to-node mapping from problem text
• Relationship-to-edge mapping
• Graph property detection (bipartite, DAG, tree, etc.)
• Suggest optimal representation (adjacency list vs matrix)
• Generate graph visualization
• Identify implicit graph structures

Target Processes

• graph-modeling
• shortest-path-algorithms
• graph-traversal
• advanced-graph-algorithms

Graph Modeling Framework

1. Entity Identification: What objects/states become nodes?
2. Relationship Analysis: What connections become edges?
3. Edge Properties: Directed? Weighted? Capacities?
4. Graph Properties: Special structure to exploit?
5. Representation Choice: List vs matrix vs implicit?

Input Schema

{
  "type": "object",
  "properties": {
    "problemDescription": { "type": "string" },
    "constraints": { "type": "object" },
    "examples": { "type": "array" },
    "outputFormat": {
      "type": "string",
      "enum": ["analysis", "code", "visualization"]
    }
  },
  "required": ["problemDescription"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "nodes": { "type": "object" },
    "edges": { "type": "object" },
    "properties": {
      "type": "object",
      "properties": {
        "directed": { "type": "boolean" },
        "weighted": { "type": "boolean" },
        "bipartite": { "type": "boolean" },
        "dag": { "type": "boolean" },
        "tree": { "type": "boolean" }
      }
    },
    "representation": { "type": "string" },
    "suggestedAlgorithms": { "type": "array" }
  },
  "required": ["success"]
}