# R04 — TOPOLOGY ANALYSIS

**Source:** `data/SKILLS_GRAPH.json` (R-02F, 2026-06-22)  
**Mutation:** NONE

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## Enumerated Graph (8 of 17 categories)

| Metric | Value |
|---|---|
| Total nodes (8 categories) | 197 |
| Total nodes (all 17 categories) | UNKNOWN — 9 categories not enumerated |
| Total edges | 0 |
| Total connected components | 197 |
| Largest connected component | 1 node |
| Average degree | 0.000 |
| Median degree | 0 |
| Maximum degree | 0 |
| Graph density | 0.000000 |
| Edge-to-node ratio | 0.000 |
| Node-to-category ratio (8 cats) | 24.6 nodes/category |
| Category coverage (enumerated) | 8 / 17 = 47.1% |
| Category coverage (all) | UNKNOWN |

## Category Node Distribution

| Category | Nodes | % of enumerated |
|---|---|---|
| 01-perception | 36 | 18.3% |
| 02-reasoning | 45 | 22.8% |
| 03-memory | 19 | 9.6% |
| 04-action-execution | 21 | 10.7% |
| 05-code | 28 | 14.2% |
| 11-web | 16 | 8.1% |
| 12-data | 18 | 9.1% |
| 13-creative | 14 | 7.1% |
| **TOTAL** | **197** | **100%** |

## Pending Categories (not yet in graph)

| Category | Status |
|---|---|
| 06-planning | Not enumerated |
| 07-tool-use | Not enumerated |
| 08-output-formatting | Not enumerated |
| 09-agent-patterns | Not enumerated |
| 10-evaluation | Not enumerated |
| 14-security | Not enumerated |
| 15-orchestration | Not enumerated |
| 16-domain-specific | Not enumerated |
| 17-infrastructure | Not enumerated |

## Topology Classification

**Current topology:** Null graph (no edges).  
A null graph is a valid graph-theoretic concept: nodes exist, no edges exist.  
Every node is an isolated vertex. There are no paths between any two nodes.  
Diameter: undefined (no paths exist).  
Radius: undefined.  
Clustering coefficient: 0 for all nodes.

## What Topology Metrics Will Look Like Post-Edges

Once edges are added (R-05 target), meaningful topology will emerge. Expected ranges based on skill graph literature:
- Average degree: 3–8 (each skill connects to 3–8 others)
- Graph density: 0.02–0.08 (sparse, as expected for domain knowledge graphs)
- Connected components: 1–5 (near-fully connected graph)
- Largest component: >90% of nodes
