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Graph Algorithms – Edmonds-Karp Maximum Flow
x402
Graph Algorithms – Edmonds-Karp Maximum Flow is a paid API for AI agents from graph-algorithms.x402tookit.com, paid per call via x402, $0.03/call, status unknown (last checked 2026-11-02).
Computes the Edmonds-Karp maximum flow from a source to a sink on a directed capacity edge list, returning flow per edge and minimum cut edges.
Price / call$0.03
Success—
StatusUnknown
How this service works
Edmonds-Karp maximum flow from a source to a sink on a capacity edge list, with flow per edge and min cut edges.
Output
Returns the maximum flow value between source and sink, an array of edge objects each showing from/to/capacity/flow, the minimum cut capacity, the list of min-cut edges (from/to/capacity), the set of nodes on the source side of the cut, and a human-readable summary. Also includes metadata like asOf timestamp and any degraded/disclaimer flags.
Example use cases
Network bandwidth bottleneck analysis
“I have a data-center network with these links and their capacities: router1,router2,100; router1,router3,60; router2,datacenter,80; router3,datacenter,70; router2,router3,20. What's the maximum throughput from router1 to the datacenter, and which links are the bottleneck?”
Supply chain maximum throughput
“I need to find how many units per day can flow from our warehouse node 'WH' to the distribution center 'DC' given these routes and their daily limits: WH,Hub1,500; WH,Hub2,300; Hub1,DC,400; Hub2,DC,350; Hub1,Hub2,150. Also tell me which routes are fully saturated.”
Minimum cut for network segmentation
“Given this internal network topology — ingress,fw1,1000; ingress,fw2,800; fw1,core,900; fw2,core,750; core,egress,1200 — what is the minimum set of links I'd need to sever to completely isolate the egress node from the ingress node, and what's the combined capacity of those cut links?”
Technical details
Endpoint
GEThttps://graph-algorithms.x402tookit.com/max-flow?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need to solve a directed maximum flow problem using the Edmonds-Karp (BFS-augmenting-path) algorithm and require both the max flow value and the minimum cut decomposition. It supports graphs up to 200 nodes and 1000 edges, making it suitable for medium-scale network flow problems in logistics, network design, or capacity planning. Prefer this over Dijkstra or Bellman-Ford sibling endpoints when the problem is about throughput/capacity rather than shortest paths.
Side effects
- Missing required parameters (edges, source, or sink) returns a validation error
- Source and sink node names are identical — the API requires them to differ
- Edge list exceeds limits (>200 nodes, >1000 edges, or >60000 characters) causes rejection
- Malformed edge format (missing capacity, non-numeric capacity, wrong delimiter) causes parse error
- Capacity values outside the 0–1e9 range may be rejected
- Network with no path from source to sink returns max flow of 0
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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