graph-structure

name	graph-structure
description	Structural graph analysis — cycles, SCCs, topological order, articulation points, bridges, k-core, dependency layers.
allowed-tools	["mcp__mycelium__get_stats","mcp__mycelium__get_graph_metrics","mcp__mycelium__detect_cycles","mcp__mycelium__get_scc_groups","mcp__mycelium__topological_sort","mcp__mycelium__find_articulation_points","mcp__mycelium__find_bridge_edges","mcp__mycelium__get_biconnected_components","mcp__mycelium__get_k_core","mcp__mycelium__get_dependency_layers","mcp__mycelium__get_strongly_connected_components","mcp__mycelium__get_wcc","mcp__mycelium__get_degree_histogram","mcp__mycelium__find_cycle_members"]
category	analysis
icon	🕸️
marketplace_examples	[{"query":"Are there circular dependencies in my imports?","tool":"mcp__mycelium__detect_cycles"},{"query":"Find the strongly connected components in the call graph","tool":"mcp__mycelium__get_scc_groups"},{"query":"Topologically sort all modules by dependency order","tool":"mcp__mycelium__topological_sort"}]

graph-structure — what shape is this graph?

This Skill bundles 14 structural-analysis tools. Where centrality ranks nodes by importance, graph-structure answers questions about the graph's overall shape: cycles, connected components, articulation points, layering.

Includes detect_cycles and get_dependency_layers — two of the top-10 most useful tools per the v0.1.1 external evaluation.

When to invoke this Skill

Use when:

• The user asks "are there circular dependencies", "what's the build order", "what would split this codebase into modules".
• Code-health audits: cycle count, dead components, modularity scores.
• Migration planning: which parts of the codebase are safe to touch independently.

Do NOT use when:

• The user wants per-node scores → centrality.
• The user wants single-symbol relationships → call-graph or reachability.

Quick examples

Developer question	Tool
"Are there circular dependencies in my imports?"	mcp__mycelium__detect_cycles
"Find the strongly connected components in the call graph"	mcp__mycelium__get_scc_groups
"Topologically sort all modules by dependency order"	mcp__mycelium__topological_sort
"Which nodes are articulation points — removing one breaks the graph?"	mcp__mycelium__find_articulation_points
"Give me overall graph metrics for this codebase"	mcp__mycelium__get_graph_metrics

Capabilities under this umbrella

get_stats — high-level summary

Node count, edge count, edge-kind histogram, language breakdown. The "is the index sane" sanity check.

mcp__mycelium__get_stats({})
→ { "nodes": 12453, "edges": 47821, "languages": ["rust", "python"], "by_edge_kind": { "calls": 28301, "imports": 11320, "extends": 213, "implements": 7987 } }

get_graph_metrics — density, diameter, average degree

⚠️ Performance: see #153. On graphs > 5k nodes, may exceed default time budget — v0.1.4 adds time_budget_ms.

detect_cycles ⭐ — find every cycle

The single most-recommended structural tool. Returns the list of cycles as ordered node sequences.

mcp__mycelium__detect_cycles({ "edge_kind": "imports", "limit": 50 })
→ { "cycles": [["src/a.py", "src/b.py", "src/a.py"], ...], "count": 3 }

get_scc_groups — strongly connected components

A cycle in the graph corresponds to an SCC of size ≥ 2. Returns the components, sorted by size.

topological_sort — dependency order

Returns nodes in topological order. Fails (or returns an error envelope) if the graph has cycles. Use detect_cycles first to confirm acyclicity.

find_articulation_points — single-node bottlenecks

Nodes whose removal disconnects the graph. Useful for identifying refactor-risk choke points.

find_bridge_edges — single-edge bottlenecks

Edges whose removal disconnects the graph. Often correspond to load-bearing imports or call chains.

get_biconnected_components — robust modules

Maximal subgraphs with no articulation points internally. These are the "robust modules" of the codebase — chunks that stay connected even when individual nodes are removed.

get_k_core — densely-connected subgraph

The k-core decomposition — useful for finding the densely-connected "hot" parts of the codebase.

get_dependency_layers ⭐ — layered ordering

Stratifies nodes by dependency depth (0 = leaves, 1 = depends only on leaves, etc.). The build-order view. One of the top-10 most useful tools.

get_scc — SCC membership for one symbol

Cheaper than get_scc_groups if you only need to know "which cycle does this symbol belong to".

get_wcc — weakly connected components

⚠️ Performance: see #153.

get_degree_histogram — degree distribution

⚠️ Performance: see #153.

find_cycle_members — which symbols are in cycles

Given an edge kind, lists every symbol that's part of any cycle.

Common chains

• "Are there circular dependencies?" → detect_cycles --edge-kind imports.
• "What order should I build/load these?" → topological_sort (after confirming no cycles).
• "What does the project decompose into?" → get_scc_groups + get_biconnected_components.
• "Where are the bottlenecks?" → find_articulation_points + find_bridge_edges.
• "How deep is this code stack?" → get_dependency_layers.

Performance

Four tools (get_graph_metrics, get_wcc, get_degree_histogram, find_articulation_points) currently exceed budget on the 926-node Mycelium-core index per #153. v0.1.4 introduces time_budget_ms + partial-result envelopes.

Equivalent CLI

mycelium detect-cycles --edge-kind imports --limit 50 --format=json
mycelium get-dependency-layers --format=json
mycelium topological-sort --edge-kind calls

Parity contract

Per RFC-0090. tests/parity.test.json uses a 5-node fixture with a small cycle to exercise cycle / SCC / topo / articulation in one place.

Cross-references

• Related Skill: centrality — for per-node importance scores.
• Related Skill: call-graph, import-graph, inheritance — for the edges that this Skill analyses.