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 sequenzia/agent-alchemy --skill graph-algorithmsgit clone --depth 1 https://github.com/sequenzia/agent-alchemyWrote 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/sequenzia/agent-alchemy/graph-algorithms)<a href="https://agentmods.dev/skills/sequenzia/agent-alchemy/graph-algorithms"><img src="https://agentmods.dev/badge/skills/sequenzia/agent-alchemy/graph-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/sequenzia/agent-alchemy/graph-algorithms"><img src="https://agentmods.dev/badge/skills/sequenzia/agent-alchemy/graph-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 | $0.00074 | $0.04545 |
| Opus 5.5 | $0.00030 | $0.01818 |
| Sonnet 5.5 | $0.00015 | $0.00909 |
| Haiku 4.5 | $0.00007 | $0.00455 |
Grade A, and why
graph-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 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 — 479 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Graph Algorithm Patterns
Graph problems appear frequently in competitive programming and technical interviews. The key challenge is recognizing which technique fits the problem structure. This reference covers eight core patterns with recognition heuristics, templates, and pitfall guides.
Pattern Recognition Table
| Trigger Signals | Technique | Typical Complexity |
|---|---|---|
| Shortest path, unweighted, fewest steps | BFS | O(V + E) |
| Explore all paths, connected components, backtracking | DFS | O(V + E) |
| Shortest path, weighted (non-negative) | Dijkstra | O((V + E) log V) |
| Dependencies, ordering, DAG | Topological Sort | O(V + E) |
| Dynamic connectivity, "are X and Y connected?" | Union-Find (DSU) | O(alpha(N)) per op |
| Minimum cost to connect all nodes | MST (Kruskal/Prim) | O(E log E) |
| Weighted shortest path with negative edges | Bellman-Ford | O(V * E) |
| Two groups, coloring, odd cycle | Bipartite Check | O(V + E) |
Constraint-to-Technique Mapping
Use V (vertices) and E (edges) bounds to narrow viable algorithms:
| Constraint Range | Viable Techniques | Notes |
|---|---|---|
| V <= 20 | Bitmask DP, brute-force BFS/DFS | Exponential OK |
| V <= 1,000, E <= 10,000 | All techniques, Floyd-Warshall for APSP | O(V^3) still feasible |
| V <= 100,000, E <= 200,000 | BFS, DFS, Dijkstra, Topo Sort, DSU, MST | Standard competitive range |
| V <= 1,000,000 | BFS, DFS, DSU, Kahn's | Avoid O(V log V) heaps if possible |
| Negative weights present | Bellman-Ford, SPFA | Dijkstra invalid |
| Dense graph (E ~ V^2) | Prim (adj matrix), Floyd-Warshall | Adjacency list Dijkstra still works |
| Edges arrive online | Union-Find | Incremental connectivity |
Individual Patterns
BFS (Breadth-First Search)
Recognition Signals
- "Shortest path" or "minimum steps" in an unweighted graph or grid
- "Level-order traversal" or "distance from source"
- Multiple starting points (multi-source BFS)
- "Nearest" something in a grid
Core Idea
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 · 479 lines · 74 tokens per session scan A c895f4a1a784
graph-algorithms is a skill published in the GitHub repository sequenzia/agent-alchemy (45 stars, last pushed 4mo ago), licensed MIT. It adds 74 tokens to every session and 4,545 once invoked, about $0.0003 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 2026-08-30.
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