# Network Flow Calculator MCP for AI Agents AI Agent Connect

> Network Flow Calculator solves maximum flow, minimum cut, and bipartite matching problems using the Edmonds-Karp algorithm. It helps you figure out how to move data or goods through a network with the most efficiency. Use it to find bottlenecks in transportation, data routing, or job scheduling.

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

## Description

The Network Flow Calculator lets you solve complex network topology problems without having to do the heavy math yourself. If you're trying to figure out how to move the most goods from a warehouse to a retail hub, you can just describe the routes and their limits. This Connector handles the underlying algorithms to give you precise answers on capacity. You can use it to find out where your system is choking by identifying the specific edges that limit your flow. It also works for assignment problems, like matching a pool of workers to a set of tasks. By bringing this into your workflow through Vinkius, you get a way to turn abstract constraints into clear numbers. You stop guessing where the bottlenecks are and start making decisions based on actual limits. It’s about moving from "I think this is the best route" to "This is the mathematically optimal flow." It handles the tedious parts of graph theory so you can focus on the actual logistics of your business.

## Tools

### compute_bipartite_matching
Matches items from one set to another, like workers to tasks. It finds the most efficient pairings possible.

### calculate_max_flow
Determines the highest volume of flow that can move from a start point to an end point. It handles complex directed graphs.

### find_min_cut
Locates the specific edges that limit your total network capacity. It shows you exactly where to expand your infrastructure.

## Prompt Examples

**Prompt:** 
```
I have a warehouse with 3 loading docks. Each dock can handle 50 units. There are 3 trucks coming in. How do I get them out fastest?
```

**Response:** 
```
Based on your warehouse layout, here is the optimal flow:

| Dock | Truck Capacity | Flow Status |
| :--- | :--- | :--- |
| Dock 1 | 50 units | **Full** |
| Dock 2 | 50 units | **Full** |
| Dock 3 | 50 units | **Full** |

**Total Throughput:** 150 units per cycle.

To maximize speed, ensure trucks are staged in a 1:1 ratio with the docks to prevent idling.
```

**Prompt:** 
```
Match these 5 delivery drivers to these 5 packages, knowing that Driver A can't do Package 3.
```

**Response:** 
```
I have calculated the most efficient matching for your drivers:

*   **Driver A** $
ightarrow$ Package 1
*   **Driver B** $
ightarrow$ Package 3
*   **Driver C** $
ightarrow$ Package 2
*   **Driver D** $
ightarrow$ Package 5
*   **Driver E** $
ightarrow$ Package 4

This matching ensures all packages are assigned while respecting Driver A's restriction.
```

**Prompt:** 
```
Where is the bottleneck in my data route if the main hub can only take 100 requests per second?
```

**Response:** 
```
I analyzed your network topology. The bottleneck is occurring at the following points:

*   **Edge (Hub $
ightarrow$ Node B):** Capacity 100 (Saturated)
*   **Edge (Node C $
ightarrow$ Node D):** Capacity 80 (Saturated)

**Action Item:** You need to increase the capacity of these two specific links to improve overall system throughput.
```

## Capabilities

### Find maximum capacity
Determine the highest possible volume that can move from a source to a destination.

### Identify bottlenecks
Locate the specific edges in a network that are restricting total flow.

### Automate resource matching
Pair items from one group to another, such as workers to specific tasks.

### Analyze directed graphs
Process complex network paths with specific capacities and directions.

### Solve assignment problems
Find the most efficient way to distribute resources across a set of requirements.

## Use Cases

### Warehouse Throughput Planning
A logistics manager asks the agent to find the max flow of a warehouse system with 5 docks and 10 loading zones. The agent uses calculate_max_flow to find the limit.

### Data Routing Optimization
A network engineer needs to know where a data center is choking. They ask the agent to find the min cut to see which cables need upgrading.

### Staffing and Shift Matching
A retail manager wants to match 20 workers to 20 different shifts. They ask the agent to use compute_bipartite_matching to find the best fit.

### Supply Chain Bottleneck Analysis
A supply chain analyst asks the agent to identify the specific links in a shipping route that limit the total units moved per day.

## Benefits

- Identify the exact edges causing delays using find_min_cut to target infrastructure upgrades.
- Calculate the maximum throughput of your data paths with calculate_max_flow to prevent system crashes.
- Automate complex job assignments with compute_bipartite_matching to ensure every worker is utilized.
- Solve transportation bottlenecks quickly without manual graph theory math.
- Get precise capacity limits for warehouse routes to improve delivery times.
- Turn abstract network constraints into clear, actionable data for your team.

## How It Works

The bottom line is you get mathematically sound answers to complex logistics and network problems without doing the manual math.

1. Define your network nodes and the capacity of the links between them.
2. Ask your agent to calculate a specific flow or a resource matching.
3. Receive the total flow value or a list of optimal pairings.

## Frequently Asked Questions

**Can the Network Flow Calculator help with my delivery routes?**
Yes. It helps you identify the maximum number of goods that can move through a specific set of paths, helping you find the most efficient routes.

**How does the Network Flow Calculator find bottlenecks?**
It identifies the specific links in your network that are operating at full capacity and restricting the flow of everything else.

**Can I use the Network Flow Calculator for job scheduling?**
Yes. It can match a pool of workers to a set of tasks to ensure the most efficient distribution of labor.

**What kind of networks can the Network Flow Calculator analyze?**
It can analyze any directed graph, including transportation networks, data routing paths, and resource allocation systems.

**Does the Network Flow Calculator handle worker assignments?**
It can automatically pair workers with tasks based on the connections you provide, maximizing the number of successful matches.

**How do I use the Network Flow Calculator for data routing?**
You describe your network nodes and their capacities, and the tool calculates the best way to move data from source to destination.

**What algorithms are used for the calculations?**
The server uses the Edmonds-Karp algorithm, which is a BFS-based implementation of the Ford-Fulkerson method, to ensure finding the shortest augmenting paths.

**How can I use this for bipartite matching?**
You can use the `compute_bipartite_matching` tool by providing two sets of nodes and their possible connections. The tool internally transforms the problem into a flow network to find the maximum number of unique pairs.

**Can this tool identify bottlenecks in my network?**
Yes, by using `find_min_cut`, you can identify the specific edges that constitute the minimum cut, which are the primary bottlenecks limiting flow from your source to your sink.