network-graph-theory

Network Graph Research — Skill & Source Corpus

Source website: https://www.cs.cornell.edu/home/kleinber/networks-book/

This repository is both a curated research corpus and a portable agent skill for network science and graph theory. It is built around Networks, Crowds, and Markets: Reasoning about a Highly Connected World by David Easley and Jon Kleinberg, augmented with David P. Williamson's Network Flow Algorithms, Polinode documentation, Wikipedia references, arXiv research records, and local synthesis guides.

Using this as a skill

The skill is compatible with Claude Code, Codex, and Cursor. Once installed, an agent will activate it for questions about graphs, centrality, community detection, diffusion/cascades, network effects, game theory on networks, web link analysis, and methodological pitfalls in network analysis.

Skill entry points:

• SKILL.md — primary skill manifest (Anthropic skill format with YAML frontmatter)
• .claude-plugin/marketplace.json — Claude Code custom marketplace catalog
• .claude-plugin/plugin.json — Claude Code plugin manifest
• skills/network-graph-theory/SKILL.md — marketplace plugin skill shim
• docs/MODES.md — INSTRUCTIVE / DESIGN / MEASURE mode router with example prompts
• AGENTS.md — universal agent instruction file
• .cursor/rules/network-graph-theory.mdc — Cursor-native rule
• docs/ACTIONS.md — playbooks for each named action, grouped by mode
• docs/TOPICS.md — fast topic-to-file lookup
• docs/QUESTIONS.md — example prompts per mode and action

Three modes of interaction:

Mode	Use it when...	Example
INSTRUCTIVE	Learning a concept, looking up a definition, comparing models	"Explain the max-flow/min-cut theorem with citation."
DESIGN	Mapping the framework onto your dataset	"Design a graph schema and metric plan from this Slack export."
MEASURE	Running an analysis on a defined graph	"Compute betweenness on this edge list and report the top 20."

What the skill can do (action catalog, by mode):

Mode	Action	Use for
INSTRUCTIVE	concept-lookup	Define a term with verbatim source quote
INSTRUCTIVE	chapter-find	Locate where a topic appears in the source
INSTRUCTIVE	source-cite	Produce a citation with chapter/line provenance
INSTRUCTIVE	theme-tour	Guided walk-through of one of the 11 themes
INSTRUCTIVE	model-compare	Contrast two models or mechanisms
INSTRUCTIVE	cross-theme-synthesis	Connect ideas across themes
INSTRUCTIVE	external-expand	Add Wikipedia/arXiv/Williamson context
INSTRUCTIVE	figure-locate	Find figures and visual elements
DESIGN	data-audit	Inventory a dataset and enumerate viable graphs
DESIGN	graph-design	Pick a graph schema (nodes, edges, weights, direction, time)
DESIGN	metric-mapping	Map research questions to metrics on the chosen graph
DESIGN	retrieval-design	Specify queries, transformations, edit policy
DESIGN	analysis-plan	Sequence the full analysis end to end
DESIGN	metric-select	Recommend a single metric for a research question
MEASURE	measure-execute	Compute a metric or run an algorithm
MEASURE	measure-validate	Null comparison, sensitivity, robustness
Cross-mode	caveat-check	Flag methodological pitfalls

See SKILL.md for the full activation guide and docs/ACTIONS.md for the playbooks.

Installation

This repo follows Claude Code's plugin marketplace format, the Agent Skills open standard, and the AGENTS.md open standard (used by Codex CLI, Cursor, Aider, OpenCode, Gemini CLI, and others). Below are explicit instructions for the primary runtimes.

Substitute /Users/neal/Desktop/network-graph-research with your own absolute path to this repo. On Linux and macOS use ln -s; on Windows use mklink /D from an Administrator shell, or copy the directory.

Claude Code custom marketplace (recommended)

Claude Code's current plugin distribution flow uses a marketplace catalog at .claude-plugin/marketplace.json, a plugin manifest at .claude-plugin/plugin.json, and namespaced plugin skills. This repo is packaged as a one-plugin marketplace whose plugin source is ./, which resolves to the repository root.

After this repository is available on GitHub, add the marketplace and install the skill from inside Claude Code:

/plugin marketplace add nealriley/network-theory-skill
/plugin install network-graph-theory@network-theory-skill
/reload-plugins