# Minimum Spanning Tree Calculator MCP for AI Agents MCP

> The Minimum Spanning Tree Calculator figures out the most efficient network connections in a graph. It uses established algorithms like Kruskal's and Prim's to find both minimum-weight (cheapest) and maximum-weight paths connecting all nodes without forming any loops. This MCP helps engineers model complex networks, from electrical grids to data flows, by identifying optimal edge sets.

## Overview
- **Category:** mathematics
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_RDp7HdTV6jL7l2yjzgw6M9KqQhoK7Tlqj178gMmL/mcp
- **Tags:** mst, kruskal, prim, graph, algorithm

## Description

When you're designing a network or analyzing connectivity, figuring out the most efficient path isn't always obvious. You need to connect every point while keeping costs low, or sometimes, maximizing capacity. This MCP gives your AI agent the tools to handle that math. Instead of manually testing thousands of edge combinations, your agent runs the calculations instantly. For instance, you can run `compute_kruskal_mst` to find the minimum cost required to connect all nodes in a given graph. If you need to start building from one specific point, `compute_prim_mst` grows the network outward using only the best available connections. It also handles the opposite case with `compute_max_spanning_tree`, maximizing connection weight when needed. Because this MCP is part of Vinkius's catalog, your agent connects once to access these critical graph algorithms and more.

## Tools

### compute_kruskal_mst
Calculates the Minimum Spanning Tree using Kruskal's algorithm on a provided edge list.

### compute_max_spanning_tree
Determines the Maximum Spanning Tree weight and edges from an input graph.

### compute_prim_mst
Calculates the Minimum Spanning Tree using Prim's algorithm, starting from a specified node.

## Prompt Examples

**Prompt:** 
```
We need to connect five remote sensor nodes using new wireless relays. The cost data is attached. What's the minimum relay setup?
```

**Response:** 
```
**Minimum Spanning Tree Results**

*   **Total Minimum Weight:** 45 units
*   **Optimal Edges Found:** 
    *   (Node A, Node B) - Cost: 12
    *   (Node C, Node D) - Cost: 8
    *   (Node A, Node C) - Cost: 10
    *   (Node E, Node B) - Cost: 15

This set of relays guarantees all nodes are connected using the least amount of material.
```

**Prompt:** 
```
Starting from the main control hub (Hub Alpha), what's the most efficient way to connect the three adjacent sub-stations? Use Prim's method.
```

**Response:** 
```
**Minimum Spanning Tree (Prim's) Starting at Hub Alpha**

*   **Connection Sequence:** 
    1.  (Hub Alpha, Sub-Station Beta) - Cost: 5
    2.  (Sub-Station Gamma, Sub-Station Beta) - Cost: 3
    3.  (Sub-Station Delta, Sub-Station Gamma) - Cost: 7
*   **Total Path Weight:** 15 units

The agent confirms that this sequence provides the lowest total cost while guaranteeing a continuous path from your specified starting point.
```

**Prompt:** 
```
We have three major data links with weights of 20, 30, and 10. What is the maximum capacity connection set we can build?
```

**Response:** 
```
**Maximum Spanning Tree Calculation**

*   The highest connectivity set uses edges:
    1.  Link A-B (Weight: 30)
    2.  Link B-C (Weight: 20)

*   **Total Maximum Weight:** 50 units

The agent confirms that by selecting these two links, you achieve the highest possible total capacity without creating a redundant loop.
```

## Capabilities

### Calculate Minimum Spanning Trees (MST)
Finds the set of lowest-weight edges that connect all points in a network without creating any cycles.

### Identify Maximum Spanning Trees
Determines the highest-weight connections possible across a graph, ignoring cycle constraints.

### Grow Networks from a Specific Node
Uses Prim's algorithm to build an MST starting at a designated node by always choosing the cheapest next connection.

## Use Cases

### Designing a Low-Cost Electrical Grid
A city planner needs to run power lines across a new development site. Asking their agent to use the Minimum Spanning Tree Calculator finds the cheapest set of routes that still guarantees every home gets electricity, preventing costly overspending on unused connections.

### Optimizing Fiber Optic Laying
A telecom company must lay new fiber optic cables connecting dozens of buildings. Using Prim's algorithm helps them plan the initial segment from their central hub, ensuring they build out efficiently without crossing redundant routes.

### Analyzing Data Dependencies in a System
A data architect needs to know the minimum set of connections required between microservices. The agent runs Kruskal's method on the service dependency graph, identifying the bare minimum links needed for system functionality.

### Maximizing Warehouse Connectivity
The facility manager wants to link several storage zones with new high-capacity conveyor belts. Using the Maximum Spanning Tree finds the configuration that maximizes total throughput capacity across all connected points.

## Benefits

- Pinpoint minimum infrastructure costs. Instead of guessing, use `compute_kruskal_mst` to find the absolute lowest-cost set of connections needed for your network.
- Optimize from a single source. If you know where construction starts, let `compute_prim_mst` guide you by growing the tree outward using only the best available connections.
- Model maximum capacity. When maximizing data throughput or power lines is key, `compute_max_spanning_tree` finds the most robust connection set.
- Eliminate redundant testing. You stop wasting time manually checking combinations; your agent handles the complex graph theory math instantly.
- Handle varying topologies. This MCP knows if your result is a single connected tree or a collection of separate, unconnected components (a spanning forest).

## How It Works

The bottom line is that you input your network map, and the MCP outputs the mathematically proven most efficient set of connections for whatever goal you define—minimum cost or maximum capacity.

1. You provide your agent with an edge list, detailing all nodes and the connecting weights (costs) between them.
2. Your agent selects which algorithm you need—Kruskal's for overall minimum cost, Prim's starting from a point, or maximum weight calculation.
3. The MCP processes the graph data and returns the specific set of edges that form the optimal tree structure, along with the total calculated weight.

## Frequently Asked Questions

**How does the Minimum Spanning Tree Calculator help with network design?**
It solves for the minimum cost way to connect every single point in your network. Instead of guessing, it uses proven algorithms to find the absolute cheapest set of required connections, saving you time and money on materials.

**Do I use this MCP if my goal is maximizing capacity instead of minimizing cost?**
Yes, but you need a specific tool. If your priority is maximum throughput or strength (like power lines), use the Maximum Spanning Tree feature to find the highest-weight connection set.

**What's the difference between Kruskal's and Prim's algorithms in this MCP?**
Kruskal's looks at all edges globally to build the cheapest network possible. Prim's is better if you have a specific starting point, as it builds the optimal network outward from that single node.

**Can I use this MCP for anything other than cables and power lines?**
Absolutely. This tool handles any graph structure with weighted edges. You can apply it to data dependencies, logistics routes, or sensor networks—anything where connectivity matters.

**Does the Minimum Spanning Tree Calculator handle multiple separate groups of nodes?**
Yes. If your network is naturally divided into unconnected sections, the MCP will identify that the result is a spanning forest, showing you all necessary connections for every isolated group.