Flow Networks

The Flow Networks client exposes a generic capacitated directed graph as a first-class resource. You create a network once, optionally clone it for what-if branches, commit structural mutations (capacity tweaks and edge appends), and solve it under whichever algorithm fits the question — without rebuilding the graph each time.

The engine itself is domain-agnostic. It speaks nodes, edges, capacities, and (optionally) per-edge costs. Domain shapes — staff scheduling, transportation, supply chains, network reliability — sit on top: write a translator that turns your domain into a CreateFlowNetworkRequest, and let the engine handle the algorithmic core.

When to reach for it

The dedicated Scheduling client wraps a flow network for one specific shape (capacitated bipartite b-matching with role stratification). Reach for flowNetworks when:

• The graph is not a scheduling shape — transport flow, escape-network capacity, project network, etc.
• You need to run different algorithms over the same graph (max-flow now, min-cut later, edge classification for sensitivity).
• You want to mutate the network between solves (raise a capacity, add a back edge) without re-uploading the whole structure.
• You need the what-if clone-and-mutate pattern that mirrors the /spaces resource.

If your problem fits the scheduling shape exactly, prefer client.scheduling.feasibility() / optimize() — same engine internally, but the SDK does the agent/day/shift translation for you.

Lifecycle

create  →  (clone)  →  (commit)  →  solve
                                  ↘ solve again with a different algorithm

create returns a stable id. Every other endpoint takes that id and returns metadata or solver output. There’s no per-call payload bloat — the network lives on the server until evicted.

Create a network

import { ReasoningLayerClient } from '@kortexya/reasoninglayer';

const client = new ReasoningLayerClient({
  baseUrl: 'https://platform.ovh.reasoninglayer.ai',
  tenantId: '...',
  auth: { mode: 'cookie' },
});

const network = await client.flowNetworks.create({
  nodes: ['s', 'a', 'b', 't'],
  source: 's',
  sink: 't',
  edges: [
    { from: 's', to: 'a', capacity: 3, label: 's-a' },
    { from: 's', to: 'b', capacity: 2, label: 's-b' },
    { from: 'a', to: 't', capacity: 2, label: 'a-t' },
    { from: 'b', to: 't', capacity: 3, label: 'b-t' },
  ],
  description: 'demo network',
});

console.log(network.id); // server-assigned UUID
console.log(network.nodeCount); // 4
console.log(network.edgeCount); // 4

Validation rules

• source and sink must appear in nodes and must be distinct.
• Every edge’s from and to must reference a declared node.
• capacity must be ≥ 0.
• label is optional but, when supplied, must be unique across the network. Labelled edges can be referenced later by commit for capacity updates.
• cost is optional; pure max-flow algorithms ignore it. Min-cost max-flow uses it as the per-unit-flow cost.

Malformed input → HTTP 400. The engine fails loudly rather than silently.

Solve

const maxFlow = await client.flowNetworks.solve(network.id, {
  algorithm: { kind: 'max_flow' },
});

console.log(maxFlow.totalFlow); // 4
for (const edge of maxFlow.edgeFlows) {
  console.log(`${edge.from} → ${edge.to}: ${edge.flow}/${edge.capacity}`);
}

The same network can be solved under any algorithm. The response narrows the relevant fields per algorithm; everything irrelevant is undefined.

Algorithm	Returns
{ kind: 'max_flow' }	totalFlow, edgeFlows
{ kind: 'min_cost_max_flow' }	totalFlow, totalCost, edgeFlows (uses edge cost)
{ kind: 'classify_edges' }	classifications (per edge: always_used / never_used / sometimes_used)
{ kind: 'classify_edges_optimal' }	classifications over optimal (min-cost) max-flow solutions
{ kind: 'min_cut' }	totalFlow, edgeFlows, minCut (source-/sink-side partition + cut edges)

Edge classification

classify_edges and classify_edges_optimal partition every forward edge into three buckets via Dulmage–Mendelsohn residual analysis:

• always_used — every max-flow solution saturates this edge. Removing it strictly reduces the max flow.
• never_used — no max-flow solution routes any flow through this edge. It can be removed at zero cost.
• sometimes_used — flow may or may not pass through; the engine has slack here.

This is the same trichotomy the scheduling engine returns over (agent, day, shift) cells, generalised to arbitrary edges. Use it for capacity-planning (“which links are bottlenecks?”) and for what-if pruning (“which edges are dead weight?”).

Min-cut

const cut = await client.flowNetworks.solve(network.id, {
  algorithm: { kind: 'min_cut' },
});

console.log(cut.minCut!.sourceSide); // ['s', 'a']
console.log(cut.minCut!.sinkSide); // ['b', 't']
console.log(cut.minCut!.cutEdges); // saturated forward edges crossing the cut

The summed capacity of cutEdges equals totalFlow — the max-flow / min-cut duality on the wire.

Mutate without rebuilding

commit lets you change the network in place. Both fields on the request are optional and may be supplied together; capacity updates apply before new edges are appended.

await client.flowNetworks.commit(network.id, {
  updateCapacities: [
    { label: 'a-t', capacity: 5 }, // bump the existing edge
  ],
  addEdges: [
    { from: 'a', to: 'b', capacity: 1 }, // append a new edge
  ],
});

// Re-solve under the same algorithm — no need to re-upload.
const replayed = await client.flowNetworks.solve(network.id, {
  algorithm: { kind: 'max_flow' },
});

updateCapacities references edges by their caller-supplied label — the unique identifier you assigned at create time (or via a previous commit that appended a labelled edge). New edges added via addEdges may also carry labels for later commits.

What-if branches with clone

clone returns a fresh network id whose graph is an independent deep copy of the source. The original is untouched; mutations on the clone don’t propagate.

const branchA = await client.flowNetworks.clone(network.id);
const branchB = await client.flowNetworks.clone(network.id);

await client.flowNetworks.commit(branchA.id, {
  updateCapacities: [{ label: 's-a', capacity: 5 }],
});
await client.flowNetworks.commit(branchB.id, {
  updateCapacities: [{ label: 's-b', capacity: 5 }],
});

const [resA, resB] = await Promise.all([
  client.flowNetworks.solve(branchA.id, { algorithm: { kind: 'max_flow' } }),
  client.flowNetworks.solve(branchB.id, { algorithm: { kind: 'max_flow' } }),
]);

// Compare resA.totalFlow vs resB.totalFlow — which capacity bump matters?

This is the same pattern as the /spaces resource for computation spaces, applied to flow networks.

Inspect a network

const snapshot = await client.flowNetworks.get(network.id);
// { id, source, sink, nodeCount, edgeCount, description? }

get returns metadata only — it doesn’t enumerate every edge. Use it to confirm a network exists, check its size after a commit, or surface the description in a UI list.

Beyond max-flow

Anything that fits “directed capacitated graph with a designated source and sink” maps onto these endpoints:

• Bipartite assignment — wire one side as source-edges, the other as sink-edges, capacities encode availability.
• Project networks — find the bottleneck path under capacity constraints.
• Network reliability — classify_edges reveals which links are always vs. never carrying flow.
• Sensitivity analysis — clone, bump a capacity, re-solve, compare.
• Min-cost transportation — supply at source, demand at sink, edge cost = transport cost per unit; solve with min_cost_max_flow.

The engine speaks edges and capacities; your domain decides what they mean.

Next steps

• See the FlowNetworks namespace API reference for the complete type-level documentation of every request and response field.
• The Scheduling guide shows the same engine wrapped for the scheduling shape — useful contrast for understanding when to use the generic resource vs. the specialised client.