# Network Flow Calculator MCP for AI Agents MCP

> Network Flow Calculator solves complex network problems using graph theory. It determines the absolute maximum flow capacity between two points, identifies critical bottlenecks (minimum cuts), and handles resource assignment tasks like scheduling or matching workers to jobs.

## Overview
- **Category:** mathematics
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_RdnwvPuYcoCX6OJTAFit8YmeHqPSTC3vBsEOyNwx/mcp
- **Tags:** max-flow, min-cut, bipartite-matching, graph-theory, edmonds-karp

## Description

Do you need to know the real limit of throughput in a data pipeline or logistics route? This MCP calculates maximum network flow using established computational methods. You can model any directed graph—from city road networks to internal server routing paths—and determine its peak capacity. Beyond just finding the highest possible flow, it pinpoints exactly where the system fails: identifying minimum cuts reveals the single most critical edge that limits performance. Furthermore, if your problem involves matching resources, like assigning specialized equipment to limited job slots or scheduling staff members to shifts, this tool handles those complex bipartite assignments. When you connect this MCP through Vinkius, your AI client gets access to a powerful computational engine that takes abstract graph theory problems and gives you concrete answers about bottlenecks, capacity, and resource limits.

## Tools

### compute_bipartite_matching
Finds the largest possible set of connections between two different groups of items or people.

### calculate_max_flow
Calculates the maximum amount of material, data, or resource that can pass from a start point to an end point in a network.

### find_min_cut
Identifies the smallest set of edges whose removal would completely disconnect a network, pinpointing its weakest link.

## Prompt Examples

**Prompt:** 
```
What's the max flow for my network connecting sources S and T?
```

**Response:** 
```
**Maximum Flow Report**

The maximum throughput capacity between Source (S) and Sink (T) is **15 units**. This calculation was performed using the Edmonds-Karp algorithm.

*   **Key Findings:** The system is limited by three primary saturated edges:
    *   (S, A): 10 units
    *   (S, B): 5 units
    *   (A, T): 8 units (or similar combination)
*   This means no matter how much capacity you add elsewhere, the total flow cannot exceed 15.
```

**Prompt:** 
```
Find the bottleneck edge in my network.
```

**Response:** 
```
**Minimum Cut Analysis**
The minimum cut is found by separating nodes {S, B} from {A, T}. The capacity of this cut is **7 units**. 

This means that adding capacity to any single link within the set {(S, A), (B, T)} will not increase the total flow above 7 until a more restrictive edge is addressed.
```

**Prompt:** 
```
I have workers and tasks. Can you match them up?
```

**Response:** 
```
**Optimal Assignment Results**

We found an optimal assignment set of size **3**. This means three unique worker-task pairs can be established simultaneously.

*   **Assignment 1:** Worker Alpha $\rightarrow$ Task Gamma (Connection Weight: 9)
*   **Assignment 2:** Worker Beta $\rightarrow$ Task Delta (Connection Weight: 7)
*   **Assignment 3:** Worker Charlie $\rightarrow$ Task Epsilon (Connection Weight: 6)
```

## Capabilities

### Determine maximum network throughput
Calculates the highest possible flow value between a designated source node and a sink node in any given network.

### Identify critical capacity bottlenecks
Pinpoints the minimum cut, revealing the specific edges or links that limit the overall data or resource throughput of a network.

### Solve complex resource assignments
Matches items from two distinct sets—like workers and tasks—to find the maximum number of viable pairings.

## Use Cases

### A global shipping company needs to optimize its major freight routes.
The logistics planner models their network of ports and rail lines. By running the max flow calculation, they confirm that a specific railway link is the critical bottleneck, allowing them to focus immediate investment on upgrading just that single point.

### A tech company needs to ensure its data center can handle peak traffic.
The data architect models all server connections. Running the min cut function reveals that a single core switch connection, not the main fiber line, is limiting overall bandwidth capacity, saving millions in unnecessary upgrades.

### A university department needs to assign limited research assistants to projects.
The operations researcher uses bipartite matching to model available students and required skills. The MCP determines the maximum number of student-project pairings possible while satisfying all prerequisite connections.

## Benefits

- Pinpoint critical failure points. Instead of guessing where a bottleneck exists, use `find_min_cut` to mathematically prove the exact link that limits network capacity.
- Determine total system throughput instantly. The MCP calculates maximum flow, giving you the absolute peak capacity for data pipelines or supply routes without manual simulation.
- Solve complex scheduling puzzles efficiently. Use `compute_bipartite_matching` to match limited resources—like specialized machines—to available jobs in seconds.
- Reduce modeling time dramatically. You don't have to run multiple simulations; you feed the constraints into this MCP and get a definitive answer on network limits.
- Validate resource allocation theories. Test if your proposed infrastructure upgrades actually increase throughput by calculating the new maximum flow after changes.

## How It Works

The bottom line is that you define the network constraints once, and the MCP calculates all the complex optimization outcomes for you automatically.

1. Define your network structure, specifying all nodes (points) and directed edges (connections), along with their current capacities.
2. Instruct your AI client to run the appropriate calculation—whether it's calculating maximum flow, finding a minimum cut, or computing a bipartite matching.
3. The MCP executes the required graph algorithm and returns precise numerical results and the specific set of limiting edges or optimal assignments.

## Frequently Asked Questions

**How does the Network Flow Calculator help with logistics routing?**
It determines the absolute capacity of your supply chain routes. Instead of just looking at distance, you find the critical choke point—the single link or facility that limits how much freight can move through your network.

**What is a minimum cut in the context of this MCP?**
A minimum cut identifies the weakest part of your system. It shows you the set of edges that, if removed, would break the connection and limit throughput to the lowest possible capacity.

**Can I use Network Flow Calculator for scheduling employees?**
Yes, it handles resource assignments using bipartite matching. You give it your pool of available staff and their required skills against a list of open jobs, and it finds the maximum number of perfect matches.

**Is this MCP better than just calculating simple averages?**
Absolutely. Simple averages ignore network structure. This tool calculates true peak capacity based on complex flow dynamics, giving you a definitive ceiling for how much your system can handle under ideal conditions.

**What kind of data does Network Flow Calculator need to run?**
It needs nodes (the locations or resources) and directed edges (the connections between them), along with the specific capacity limit for each connection. That's all it requires.