Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hajibabaie/combinatorial-optimization-skills --skill network-flow-optimizationgit clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/network-flow-optimization)<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/network-flow-optimization"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/network-flow-optimization/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/network-flow-optimization"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/network-flow-optimization.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00148 | $0.11502 |
| Opus 5.5 | $0.00059 | $0.04601 |
| Sonnet 5.5 | $0.00030 | $0.02300 |
| Haiku 4.5 | $0.00015 | $0.01150 |
Grade A, and why
network-flow-optimization scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 1mo ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 891 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Network Flow Optimization
You are an expert in network flow optimization: shortest paths, maximum flow, minimum-cost flow, and multicommodity flow. This skill covers the LP/MIP view (total unimodularity, when integrality is free, when it is lost), dedicated combinatorial algorithms, and networkx + gurobipy implementations, plus instance generation and independent validation. Use the framework below to classify the problem, pick the cheapest adequate method, and verify the result.
Initial Assessment
Establish these points before formulating or recommending a method:
- Which flow problem is it, exactly? Shortest path, max flow, min-cost flow, transshipment, or multicommodity? Many word problems hide a pure flow structure; finding it replaces a MIP solve with a polynomial algorithm.
- Single commodity or several? One commodity keeps total unimodularity and free integrality. Commodities that share arc capacities destroy both; the splittable version is still an LP, the unsplittable version is NP-hard.
- Side constraints. Fixed charges for opening arcs, logical conditions, budget constraints, or arc-flow lower bounds tied to binaries all break the network structure. Plan for a MIP the moment one appears.
- Sizes. Nodes n, arcs m, commodities K. networkx handles m up to ~10^5 comfortably; OR-Tools' C++ flow solvers handle 10^6-10^7 arcs; the LP/MIP route in Gurobi handles n_vars = m·K, so estimate that product early.
- Sign of arc costs. Negative costs rule out plain Dijkstra. Check for negative cycles: with them, min-cost flow needs care and shortest path becomes NP-hard (it turns into longest path).
- Directed or undirected. Most algorithms and all formulations below assume directed arcs. Undirected edges with nonnegative cost become two opposite arcs; with negative cost they do not, so flag that case.
- Data type. Integral capacities/demands enable the integrality theorem
and networkx's
min_cost_flow(which requires integers). Float data must be scaled, or you must use the LP route. - Balance check. Do supplies equal demands (sum of b_i = 0)? If not, decide where the slack goes (dummy node, inequality balances).
- Solve count. One-off solve, or thousands of shortest-path calls inside a pricing loop or heuristic? Embedded use changes tooling (reusable arrays, scipy.csgraph, warm potentials).
- Solver availability. Gurobi licensed? If not, networkx + OR-Tools + scipy cover everything here; the LP/MIP models run on HiGHS.
- Deliverable. Flow values only, or also duals/potentials, the min cut, and a sensitivity story? This decides LP route vs pure algorithm.
- Validation path. Agree up front that every reported flow passes the independent feasibility and objective check provided below.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 1mo ago First seen · 891 lines · 148 tokens per session scan A 3234e550b595
network-flow-optimization is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (14 stars, last pushed 4mo ago), licensed MIT. It adds 148 tokens to every session and 11,502 once invoked, about $0.0006 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-31.
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