What is graph-algorithms?

Reference instructions for solving graph problems, where a graph is a set of points connected by links. They cover methods for finding routes, dependencies, connected groups, and minimum-cost connections.

Use them for breadth-first or depth-first searches, shortest paths, minimum spanning trees, dependency ordering, connectivity analysis, and related graph algorithms.

They provide established approaches for common graph tasks instead of requiring each solution to be designed from scratch. The guide covers both simple and advanced cases.

graph-algorithms — Skill for Claude Code by Tyler-R-Kendrick

Install

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.

Any agent

npx skills add Tyler-R-Kendrick/agent-skills --skill graph-algorithms

Clone the repo

git clone --depth 1 https://github.com/Tyler-R-Kendrick/agent-skills

Made for: Claude Code.

Or install agent-skills, the plugin that ships this one along with the rest of its 57 skills.

Wrote 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.

README.md

[![agentmods](https://agentmods.dev/badge/skills/tyler-r-kendrick/agent-skills/graph-algorithms/github.svg)](https://agentmods.dev/skills/tyler-r-kendrick/agent-skills/graph-algorithms)

Your own site

<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.

Your own site · 80×15

<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>

Per session 129 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.

When invoked 2,501 The whole file, excluding the scripts and references it only reads on demand.

Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.

Origin original No closer match found in the catalogue.

Token cost

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 5.5	$0.00052	$0.01000
Sonnet 5.5	$0.00026	$0.00500
Haiku 4.5	$0.00013	$0.00250

Measured 2mo ago against content hash 1bf315ac5e83, method: parsed. Prices are Anthropic first-party input rates as of 2026-10-07, from the pricing page.

Security

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 2mo 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.

skills/dev/algorithms/graph-algorithms/SKILL.md · 242 lines

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)

Read the full file on GitHub · 242 lines

Files

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.

Changes

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.

2mo ago First seen · 242 lines · 129 tokens per session scan A 1bf315ac5e83

Subscribe to this mod's changes

graph-algorithms is a skill published in the GitHub repository Tyler-R-Kendrick/agent-skills (13 stars, last pushed 5mo ago), licensed MIT. It adds 129 tokens to every session and 2,501 once invoked, about $0.0005 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.

Learning and teaching

graph-algorithms next to 6 skills from other repositories
Mod	Type	Stars	Last push	Licence	Scan	Tokens	Works with
graph-algorithmsTyler-R-Kendrick/agent-skills	Skill	13	5mo ago	MIT	A	129	Claude Code
hr-onboardingnexu-io/open-design	Skill	106k	yesterday	Apache-2.0	A	62	Claude Code, Codex
book-mirrorgarrytan/gbrain	Skill	32k	yesterday	MIT	A	138	Claude Code
exam-forecastanthropics/claude-for-legal	Skill	9.9k	3d ago	Apache-2.0	A	73	Claude Code
lean-formalizewanshuiyin/Auto-claude-code-research-in-sleep	Skill	19k	3d ago	MIT	A	81	Claude Code
eli5companion-inc/feynman	Skill	10k	6d ago	MIT	A	63	Claude Code, Codex
deck-course-modulenexu-io/html-anything	Skill	9.4k	25d ago	Apache-2.0	A	25	Claude Code, Codex