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 hamzabellouch/agent-skills --skill graph-theory-and-algorithmsgit clone --depth 1 https://github.com/hamzabellouch/agent-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/hamzabellouch/agent-skills/graph-theory-and-algorithms)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/graph-theory-and-algorithms"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/graph-theory-and-algorithms/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/hamzabellouch/agent-skills/graph-theory-and-algorithms"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/graph-theory-and-algorithms.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 | $0.00061 | $0.00543 |
| Opus 5.5 | $0.00024 | $0.00217 |
| Sonnet 5.5 | $0.00012 | $0.00109 |
| Haiku 4.5 | $0.00006 | $0.00054 |
Grade A, and why
graph-theory-and-algorithms 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 today.
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.
What it actually says
Graph Theory & Algorithms
Basics
- Graph G = (V,E); degree sum = 2|E| (handshake); paths, cycles, connected components; bipartite iff no odd cycle; trees: connected acyclic, |E| = |V| - 1; forests; rooted trees.
- Euler: circuit exists iff connected and all degrees even; Hamiltonian cycles (NP-complete; Dirac and Ore conditions).
- Planarity: Euler's formula V - E + F = 2; E <= 3V - 6; Kuratowski (K5, K3,3 minors); Four Color Theorem; chromatic number chi(G) <= Delta + 1, Brooks theorem; chromatic polynomial.
- Matchings: Hall's theorem; Konig (bipartite max matching = min vertex cover); Tutte; Hungarian algorithm for assignment.
- Connectivity: Menger's theorem; max-flow min-cut (Ford-Fulkerson, Edmonds-Karp, Dinic).
- Spectral: adjacency and Laplacian eigenvalues; number of spanning trees via Kirchhoff's matrix-tree theorem; expanders; random walks.
Algorithms
- BFS/DFS O(V+E); topological sort; strongly connected components (Tarjan/Kosaraju).
- Shortest paths: Dijkstra (non-negative weights) O((V+E) log V), Bellman-Ford (negative edges), Floyd-Warshall O(V^3), A*.
- Minimum spanning tree: Kruskal (union-find) and Prim.
- Network flow, bipartite matching, 2-SAT, LCA.
- Complexity: P, NP, NP-complete (SAT, 3-coloring, clique, vertex cover, TSP decision, Hamiltonian path); reductions; approximation algorithms (2-approx vertex cover); P vs NP open.
Random & extremal graphs
Erdos-Renyi G(n,p) threshold phenomena (connectivity at p = ln n/n); small-world and scale-free networks; Turan; Ramsey; graph limits.
Proof/solution pattern
Pick the right invariant (degree, parity, coloring), use induction on vertices/edges, double count edges, apply extremal choice (longest path), or reduce to a known algorithm.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
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.
- today First seen · 28 lines · 61 tokens per session scan A d39ccc58036c
graph-theory-and-algorithms is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 61 tokens to every session and 543 once invoked, about $0.0002 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 2026-10-17.
Other skills, from other repositories
polya-docs
Phase 6 of the Pólya Heuristic Coder: Technical Documentation via Diátaxis Framework (Tutorials, How-To Guides, Reference, Explanation).
agricultural-sciences-professor
Use when a task needs the judgment of a tenure-track or tenured Agricultural Sciences faculty member at a land-grant university — deciding whether to submit a grant this cycle versus wait, allocating time across the teaching/research/extension appointment split, diagnosing a stalled graduate student or field trial, or…
adapted-physical-education-specialist
Use when a task needs the judgment of an Adapted Physical Education Specialist — writing a legally-defensible PE present level and annual goal from motor/fitness assessment data, choosing the right test battery and alternate items for a student's mobility profile, recommending a placement step on the PE…
area-ethnic-cultural-studies-professor
Use when a task needs the judgment of an Area, Ethnic, or Cultural Studies Professor — designing a joint-appointment course load across two departments, prepping a tenure or mid-tenure review file for interdisciplinary scholarship, deciding whether a course survives an enrollment or political-pressure threat…
art-drama-music-professor-postsecondary
Use when a task needs the judgment of a Postsecondary Art, Drama, or Music Professor — diagnosing a jury/crit score that contradicts a semester of formative work, building a studio-art or performance tenure dossier around exhibitions and productions instead of publications, staffing applied one-on-one lessons or crit…
career-technical-education-teacher-postsecondary
Use when a task needs the judgment of a Career/Technical Education Teacher, Postsecondary — defending a shrinking trade or health-science program against a cutback decision, backward-mapping a shop or lab curriculum to an industry credential's exam blueprint, resolving a competency-based grading dispute where a…