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 Tyler-R-Kendrick/agent-skills --skill graph-algorithmsgit clone --depth 1 https://github.com/Tyler-R-Kendrick/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/tyler-r-kendrick/agent-skills/graph-algorithms)<a href="https://agentmods.dev/skills/tyler-r-kendrick/agent-skills/graph-algorithms"><img src="https://agentmods.dev/badge/skills/tyler-r-kendrick/agent-skills/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/tyler-r-kendrick/agent-skills/graph-algorithms"><img src="https://agentmods.dev/badge/skills/tyler-r-kendrick/agent-skills/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 | $0.00129 | $0.02501 |
| Opus 5 | $0.00064 | $0.01251 |
| Sonnet 5 | $0.00026 | $0.00500 |
| Haiku 4.5 | $0.00013 | $0.00250 |
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 10d 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 — 242 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Graph Algorithms
Overview
Graph algorithms solve problems on structures composed of vertices (nodes) and edges (connections). They are central to network analysis, scheduling, routing, social networks, compilers, and countless other domains. Knuth addresses graph algorithms across The Art of Computer Programming, particularly in Volumes 1, 4A, and 4B, covering everything from basic traversal to combinatorial graph problems.
Graph Types
| Type | Description |
|---|---|
| Directed (digraph) | Edges have direction: (u, v) does not imply (v, u) |
| Undirected | Edges are bidirectional: {u, v} connects both ways |
| Weighted | Edges carry numeric weights (costs, distances) |
| Unweighted | All edges are equivalent (or weight = 1) |
| Cyclic | Contains at least one cycle |
| Acyclic | Contains no cycles. A directed acyclic graph is a DAG |
| Connected | Every vertex is reachable from every other (undirected) |
| Strongly connected | Every vertex reachable from every other via directed paths |
Traversal Algorithms
Breadth-First Search (BFS)
Explores vertices level by level, visiting all neighbors before moving deeper. Uses a queue.
- Time: O(V + E)
- Space: O(V)
- Use for: Shortest path in unweighted graphs, level-order traversal, checking bipartiteness, finding connected components.
BFS(G, source):
create queue Q
mark source as visited
Q.enqueue(source)
while Q is not empty:
u = Q.dequeue()
for each neighbor v of u:
if v is not visited:
mark v as visited
Q.enqueue(v)
Depth-First Search (DFS)
Explores as deep as possible along each branch before backtracking. Uses a stack (or recursion).
- Time: O(V + E)
- Space: O(V)
- Use for: Cycle detection, topological sort, finding connected/strongly connected components, path finding, maze solving.
DFS(G, source):
mark source as visited
for each neighbor v of source:
if v is not visited:
DFS(G, v)
What ships with it
11 files 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.
- AGENTS.md 8.8 KB
- metadata.json 845 B
- README.md 752 B
- rules/_sections.md 1.5 KB
- rules/_template.md 375 B
- rules/graph-algorithms-always-choose-the-simplest-algorithm-that-handles-your.md 525 B
- rules/graph-algorithms-consider-whether-the-graph-is-a-dag-many-problems.md 478 B
- rules/graph-algorithms-for-a-invest-time-in-designing-a-good-heuristic-the.md 436 B
- rules/graph-algorithms-for-sparse-graphs-adjacency-list-representation-is-almost.md 505 B
- rules/graph-algorithms-reference-knuth-s-taocp-for-rigorous-mathematical-analysis.md 454 B
- rules/graph-algorithms-when-implementing-kruskal-s-always-use-union-find-with.md 462 B
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.
- 10d ago First seen · 242 lines · 129 tokens per session scan A 1bf315ac5e83
graph-algorithms is a skill published in the GitHub repository Tyler-R-Kendrick/agent-skills (11 stars, last pushed 3mo ago), licensed MIT. It adds 129 tokens to every session and 2,501 once invoked, about $0.0006 per session on Opus 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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