graph

name	graph
description	Analyze the vault's knowledge graph. Subcommands: orphans, density, bridges, synthesis, traverse, clusters, stats.
tags	["analysis","graph","connections"]

Skill: graph

Delegates to: @ars-contexta:graph-analyst

Trigger

Invoke this skill for structural analysis of the vault's knowledge graph. Where health checks correctness, graph reveals topology, centrality, and emergent structure.

Arguments

• orphans — find notes with zero incoming links
• density — compute link metrics across the vault
• bridges — find high-betweenness notes (critical connectors)
• synthesis — surface connection opportunities between unlinked but related notes
• traverse <note> — explore the 2-hop neighborhood of a specific note
• clusters — detect topic groupings from link density
• stats — overall graph metrics summary

If no argument is provided, run stats.

Behavior

Use ripgrep as the primary query engine for all graph operations. Build link maps by grepping for [[ patterns across the vault.

Subcommand: orphans Find all notes in the domain notes folder. For each, check whether any other note contains [[{note title}]]. Notes with zero incoming references are orphans. Report the full list with note title and creation date. Notes in self/ and ops/ are excluded from orphan analysis.

Subcommand: density Compute:

• Total notes in vault
• Total wiki-links (outgoing)
• Average outgoing links per note
• Average incoming links per note
• Median outgoing links
• Notes with zero outgoing links (no connections made)
• Notes with zero incoming links (orphans, see above)
• Link density ratio: total links / (n × (n-1)) where n = note count

Subcommand: bridges Find notes with high betweenness centrality: notes that appear on many shortest paths between other notes. Approximate via incoming link count × unique referencing notes. High-betweenness notes are structural dependencies — if removed, the graph would fragment. List the top 10 by estimated betweenness.

Subcommand: synthesis Find pairs or clusters of notes that share significant keyword overlap but have no wiki-link between them. These are candidates for explicit connection or synthesis. Use ripgrep to extract key terms from titles and descriptions, then find unlinked note pairs with ≥3 shared significant terms. Report top 10 opportunities with explanation of the shared theme.

Subcommand: traverse <note> Map the 2-hop neighborhood of the specified note:

• Hop 0: the note itself
• Hop 1: all notes the target links to + all notes that link to the target
• Hop 2: all notes connected to hop-1 nodes (excluding already-listed)

Output as a structured list with relationship direction indicated. Cap at 50 nodes to keep output readable.

Subcommand: clusters Detect emergent topic groupings by link density. Notes that are densely interconnected among themselves and sparsely connected to other groups form a cluster. Approximate via MOC co-membership combined with direct link overlap. Report clusters with member count and a suggested cluster label derived from member titles.

Subcommand: stats Print a one-page overview:

Knowledge Graph Stats — {YYYY-MM-DD}

Notes:        {n} total, {n} in notes/, {n} in self/, {n} in ops/
Links:        {n} total wiki-links, {avg} per note
Orphans:      {n} notes ({pct}%) with zero incoming links
Top hubs:     {top 5 notes by incoming link count}
MOCs:         {n} topic maps, avg {n} members each
Clusters:     {n} detected
Graph age:    oldest note {date}, newest note {date}