centrality

name	centrality
description	Rank symbols by importance — PageRank, betweenness, fan-in/out, hub detection, top-file diagnostics.
allowed-tools	["mcp__mycelium__rank_symbols","mcp__mycelium__get_top_files","mcp__mycelium__get_most_connected","mcp__mycelium__get_hub_symbols","mcp__mycelium__get_fan_out_rank","mcp__mycelium__get_fan_in_rank","mcp__mycelium__get_betweenness_centrality","mcp__mycelium__get_closeness_centrality","mcp__mycelium__get_degree_centrality","mcp__mycelium__get_clustering_coefficient","mcp__mycelium__get_eccentricity","mcp__mycelium__page_rank","mcp__mycelium__get_harmonic_centrality","mcp__mycelium__get_neighbor_similarity"]
category	analysis
icon	⭐
marketplace_examples	[{"query":"Which symbols are most critical to this codebase?","tool":"mcp__mycelium__rank_symbols"},{"query":"What are the top 10 most-connected files?","tool":"mcp__mycelium__get_top_files"},{"query":"Rank all functions by fan-in","tool":"mcp__mycelium__get_fan_in_rank"}]

centrality — who matters in this codebase

This Skill bundles 14 ranking and importance-scoring tools. Where call-graph and reachability answer "what's connected to what", centrality answers "which of those connections matter most".

Includes rank_symbols and get_top_files — 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 "what are the most important symbols in this codebase", "which files do I need to know first", "where are the hubs".
• Onboarding into an unfamiliar project — surface the top-ranked files and symbols first.
• Identifying refactor pressure points — high-betweenness symbols are bottlenecks.

Do NOT use when:

• The user wants raw connectivity, not scores → use call-graph or reachability.
• The user wants a specific symbol's neighborhood → use get_symbol_neighborhood from reachability.

Quick examples

Developer question	Tool
"Which symbols are most critical to this codebase?"	mcp__mycelium__rank_symbols
"What are the top 10 most-connected files?"	mcp__mycelium__get_top_files
"Rank all functions by fan-in"	mcp__mycelium__get_fan_in_rank
"Compute PageRank for this codebase"	mcp__mycelium__page_rank
"Find hub symbols with high in-degree"	mcp__mycelium__get_hub_symbols

Capabilities under this umbrella

rank_symbols ⭐ — overall importance ranking

The single most-recommended tool for "what should I look at first" in any codebase. Combines centrality scores into one ranking.

mcp__mycelium__rank_symbols({ "limit": 20 })

get_top_files ⭐ — most important files

Same idea, file-level. Surfaces the highest-leverage files for onboarding or audit.

mcp__mycelium__get_top_files({ "limit": 10 })

Caveat: a file appearing here may be a "god file" — high importance can mean high coupling, which is often a smell.

get_most_connected — total-degree ranking

Symbols with the most edges across all kinds. Closely related to degree_centrality but conveniently sorted descending and limited.

get_hub_symbols — high in-degree

Symbols that everyone depends on. Reverse of get_dead_symbols from call-graph. Combine with get_top_files to find the load-bearing parts of the codebase.

get_fan_out_rank — symbols that call many things

Useful for "what's the most coupling-heavy code" — high fan-out often means a coordinator or orchestrator. Sometimes a refactor target.

get_fan_in_rank — symbols that many things call

Inverse of fan-out. Symbols here are the most leveraged — changes break the most callers.

betweenness_centrality — bottleneck detection

Returns the number of shortest paths passing through each symbol. High betweenness = bottleneck; if it breaks, many flows are disrupted.

mcp__mycelium__betweenness_centrality({ "edge_kind": "calls", "limit": 20 })

Expensive on large graphs — see #153 for performance bounds.

closeness_centrality — distance from everything

Symbols with low average distance to every other symbol. The "well-connected" middle of the graph.

degree_centrality — raw in/out degree

The simplest centrality. Often a good first pass before reaching for more expensive measures.

clustering_coefficient — local triangle density

How tightly clustered is a symbol's neighborhood? High = cohesive module; low = bridge.

eccentricity — farthest distance to any other symbol

The maximum shortest-path distance from the symbol to any other. Eccentricity is high for symbols "on the edge" of the call graph.

page_rank — PageRank with edge kinds

Classic PageRank, edge-kind-parameterized. Heavier than degree_centrality but more informative for asymmetric graphs.

Expensive on large graphs — see #153.

harmonic_centrality — robust closeness

Closeness centrality variant that gracefully handles disconnected graphs. Use this instead of closeness_centrality if the project has unreachable subgraphs.

neighbor_similarity — find related symbols

Given a symbol, returns symbols with overlapping neighborhoods. Useful for "find me other things like this".

Common chains

• "Where do I start understanding this codebase?" → get_top_files then rank_symbols.
• "Where will breakage cascade if I change something?" → get_fan_in_rank (downstream blast) + betweenness_centrality (cross-cut bottlenecks).
• "Find similar code" → neighbor_similarity.

Performance notes

page_rank, betweenness_centrality, wcc-class algorithms are heavy on large graphs. Issue #153 tracks this; v0.1.4 introduces partial-result envelopes and a time_budget_ms parameter.

Equivalent CLI

mycelium rank-symbols --limit 20 --format=json               # top callee symbols (Calls)
mycelium rank-symbols --edge-kind imports --limit 20          # most-imported symbols
mycelium rank-symbols --edge-kind extends --limit 10          # most-extended base classes
mycelium get-top-files --limit 10
mycelium page-rank --edge-kind calls --limit 20

Parity contract

Per RFC-0090. tests/parity.test.json asserts byte-equality on a small fixture for each capability.

Cross-references

• Related Skill: call-graph, reachability — for the connectivity these tools rank.
• Related Skill: graph-structure (planned) — for cycle and SCC detection that often combines with centrality.