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README.md

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 Dependency graph of [Mathlib](https://github.com/leanprover-community/mathlib4) (commit [`534cf0b`](https://github.com/leanprover-community/mathlib4/commit/534cf0b), 2 Feb 2026), the largest formal mathematics library for Lean 4 (`v4.28.0-rc1`).
 
-Three dependency layers (declarations, modules, namespaces) with precomputed network metrics.
+Three dependency layers (declarations, modules, namespaces), each with nodes, edges, and precomputed network metrics.
 
 ## Quick Stats
 
 | | Declarations | Modules | Namespaces (k=2) |
 |---|---|---|---|
 | Nodes | 308,129 | 7,564 | 10,097 |
-| Edges | 8,436,366 | 20,881 | 332,081 |
-| DAG depth | 83 | 154 | 7 |
+| Edges | 8,436,366 | 20,881 | 332,081 (weighted) |
+| DAG depth | 83 | 154 | 7 (after SCC condensation) |
 | Louvain modularity | 0.478 | 0.610 | 0.270 |
 | Synthesized edges | 74.2% | — | — |
-| Cross-namespace edges | — | — | 85.8% |
+| In cycles | 5,732 nodes | 0 (DAG) | 6,055 nodes (38 SCCs) |
 
 ## Files
 
-### Raw Graph Data
+### Raw Data (v1)
 
 | File | Rows | Description |
 |------|------|-------------|
-| `mathlib_nodes.csv` | 317,655 | Declarations before deduplication (name, kind, module) |
-| `mathlib_edges.csv` | 8,436,366 | Declaration dependencies (source, target, is_explicit, is_simplifier) |
-| `nodes.csv` | 633,364 | Full environment including Lean core and Std |
-| `edges.csv` | 10,889,011 | Full environment edges |
+| `mathlib_edges.csv` | 8,436,366 | Declaration dependency edges |
+| `mathlib_nodes.csv` | 317,655 | Declarations before deduplication |
+| `nodes.csv` / `edges.csv` | 633K / 10.9M | Full environment (Lean + Std + Mathlib) |
 | `mechanisms.ndjson` | — | Lean language mechanism extractions |
 | `tactic_usage.ndjson` | — | Per-declaration tactic usage profiles |
 
-### Module and Namespace Graphs (v2)
+### Three-Layer Graphs (v2)
 
-| File | Rows | Description |
-|------|------|-------------|
-| `v2/mathlib_module_nodes.csv` | 7,564 | Module (source file) list with decl_count |
-| `v2/mathlib_module_edges.csv` | 20,881 | Module import edges (source, target) |
-| `v2/mathlib_namespace_nodes_k2.csv` | 10,097 | Depth-2 namespace list with decl_count |
-| `v2/mathlib_namespace_edges_k2.csv` | 332,081 | Namespace edges with weight (aggregated from declaration edges) |
+Each layer has `nodes.csv`, `edges.csv`, and `metrics.csv`:
 
-### Enriched Metrics (v2)
+| Folder | Nodes | Edges | Metrics | Description |
+|--------|-------|-------|---------|-------------|
+| `v2/declaration/` | 308,129 | (use root `mathlib_edges.csv`) | 308,129 x 11 | Theorems, definitions, and other named constants |
+| `v2/module/` | 7,564 | 20,881 | 7,564 x 10 | Source files linked by `import` statements |
+| `v2/namespace/` | 10,097 | 332,081 | 10,097 x 11 | Depth-2 dotted-name prefixes, weighted edges |
 
-| File | Rows | Columns | Description |
-|------|------|---------|-------------|
-| `v2/mathlib_nodes_enriched.csv` | 308,129 | 11 | Deduplicated declarations with network metrics |
-| `v2/mathlib_modules.csv` | 7,564 | 10 | Per-module precomputed metrics |
-| `v2/mathlib_namespaces_k2.csv` | 10,097 | 9 | Per-namespace precomputed metrics |
-| `v2/mathlib_summary.json` | — | — | Headline statistics for all three graph levels |
+`v2/summary.json` contains headline statistics for all three levels.
 
 ## Quick Start
 
 ```python
 from datasets import load_dataset
 
-nodes = load_dataset("MathNetwork/MathlibGraph",
-                     data_files="v2/mathlib_nodes_enriched.csv", split="train").to_pandas()
+# Declaration level
+decl = load_dataset("MathNetwork/MathlibGraph",
+                    data_files="v2/declaration/metrics.csv", split="train").to_pandas()
 edges = load_dataset("MathNetwork/MathlibGraph",
                      data_files="mathlib_edges.csv", split="train").to_pandas()
 
-print(f"Declarations: {len(nodes):,}, Edges: {len(edges):,}")
-print(nodes.nlargest(5, "pagerank")[["name", "kind", "in_degree", "pagerank"]])
+# Module level
+mod_nodes = load_dataset("MathNetwork/MathlibGraph",
+                         data_files="v2/module/nodes.csv", split="train").to_pandas()
+mod_edges = load_dataset("MathNetwork/MathlibGraph",
+                         data_files="v2/module/edges.csv", split="train").to_pandas()
+
+# Namespace level
+ns_nodes = load_dataset("MathNetwork/MathlibGraph",
+                        data_files="v2/namespace/nodes.csv", split="train").to_pandas()
+ns_edges = load_dataset("MathNetwork/MathlibGraph",
+                        data_files="v2/namespace/edges.csv", split="train").to_pandas()
 ```
 
 ## Schema
 
-### v2/mathlib_module_nodes.csv
-
-| Column | Type | Description |
-|--------|------|-------------|
-| module | str | Dotted module name (e.g., `Mathlib.Algebra.Group.Defs`) |
-| decl_count | int | Number of declarations defined in this module |
+### v2/declaration/nodes.csv
 
-### v2/mathlib_module_edges.csv
+Deduplicated from `mathlib_nodes.csv` (317,655 to 308,129 rows; 9,526 `@[to_additive]` mirrors removed).
 
 | Column | Type | Description |
 |--------|------|-------------|
-| source | str | Importing module |
-| target | str | Imported module |
+| name | str | Fully qualified declaration name |
+| kind | str | theorem, definition, abbrev, inductive, constructor, opaque, axiom, or quotient |
+| module | str | Parent namespace (null for 30,944 Lean core declarations) |
 
-### v2/mathlib_namespace_nodes_k2.csv
+### v2/declaration/metrics.csv
+
+All columns from `nodes.csv` plus:
 
 | Column | Type | Description |
 |--------|------|-------------|
-| namespace | str | Depth-2 namespace (e.g., `Mathlib.Algebra`) |
-| decl_count | int | Declarations in this namespace |
+| namespace_depth2 | str | First 2 dot-separated components (e.g., `Mathlib.Algebra`) |
+| namespace_depth3 | str | First 3 dot-separated components |
+| in_degree | int | Declarations that depend on this one |
+| out_degree | int | Declarations this one depends on |
+| pagerank | float | PageRank (alpha=0.85) |
+| betweenness | float | Betweenness centrality (k=500, seed=42) |
+| community_id | int | Louvain community |
+| dag_layer | int | Topological depth; -1 for 5,732 nodes in cycles |
 
-### v2/mathlib_namespace_edges_k2.csv
+### v2/module/nodes.csv
 
 | Column | Type | Description |
 |--------|------|-------------|
-| source | str | Source namespace |
-| target | str | Target namespace |
-| weight | int | Number of declaration-level edges between these namespaces |
+| module | str | Dotted module name (e.g., `Mathlib.Algebra.Group.Defs`) |
+| decl_count | int | Declarations defined in this source file |
 
-### v2/mathlib_nodes_enriched.csv
+### v2/module/edges.csv
 
 | Column | Type | Description |
 |--------|------|-------------|
-| name | str | Fully qualified declaration name |
-| kind | str | One of: theorem, definition, abbrev, inductive, constructor, opaque, axiom, quotient |
-| module | str | Parent namespace of the declaration (null for 30,944 Lean core declarations) |
-| namespace_depth2 | str | First 2 dot-separated name components (e.g., `Mathlib.Algebra`) |
-| namespace_depth3 | str | First 3 dot-separated name components |
-| in_degree | int | Declarations that depend on this one |
-| out_degree | int | Declarations this one depends on |
-| pagerank | float | PageRank (alpha=0.85) |
-| betweenness | float | Betweenness centrality (sampled, k=500, seed=42) |
-| community_id | int | Louvain community assignment |
-| dag_layer | int | Topological depth; -1 for 5,732 nodes in cycles |
+| source | str | Importing module |
+| target | str | Imported module |
 
-### v2/mathlib_modules.csv
+### v2/module/metrics.csv
 
 | Column | Type | Description |
 |--------|------|-------------|
-| module | str | Dotted module name (e.g., `Mathlib.Algebra.Group.Defs`) |
-| decl_count | int | Declarations in this module (235K jixia coverage) |
+| module | str | Module name |
+| decl_count | int | Declarations (235K jixia coverage) |
 | in_degree | int | Modules that import this one |
 | out_degree | int | Modules this one imports |
 | pagerank | float | PageRank on module import graph |
-| betweenness | float | Betweenness centrality (exact, no sampling) |
+| betweenness | float | Betweenness centrality (exact) |
 | dag_layer | int | Topological depth in module DAG |
-| community_id | int | Louvain community assignment |
-| cohesion | float | Fraction of edges that stay within the module |
-| import_utilization_median | float | Median fraction of imported declarations actually used |
+| community_id | int | Louvain community |
+| cohesion | float | Fraction of declaration edges staying within module |
+| import_utilization_median | float | Median fraction of imported declarations used |
 
-### v2/mathlib_namespaces_k2.csv
+### v2/namespace/nodes.csv
 
 | Column | Type | Description |
 |--------|------|-------------|
 | namespace | str | Depth-2 namespace (e.g., `Mathlib.Algebra`) |
 | decl_count | int | Declarations in this namespace |
-| in_degree | int | Unweighted in-degree in namespace graph |
+| in_cycle | bool | True if this namespace is in a strongly connected component |
+| scc_id | int | SCC identifier (-1 if not in a cycle) |
+
+### v2/namespace/edges.csv
+
+| Column | Type | Description |
+|--------|------|-------------|
+| source | str | Source namespace |
+| target | str | Target namespace |
+| weight | int | Number of declaration-level edges between these namespaces |
+
+### v2/namespace/metrics.csv
+
+| Column | Type | Description |
+|--------|------|-------------|
+| namespace | str | Depth-2 namespace |
+| decl_count | int | Declarations in this namespace |
+| in_degree | int | Unweighted in-degree |
 | out_degree | int | Unweighted out-degree |
-| edge_weight_sum | int | Sum of declaration-level edges involving this namespace |
+| edge_weight_sum | int | Total declaration edges involving this namespace |
 | pagerank | float | Weighted PageRank (alpha=0.85) |
 | betweenness | float | Weighted betweenness (k=300, seed=42) |
-| community_id | int | Louvain community on weighted undirected graph |
+| community_id | int | Louvain community (weighted undirected) |
 | cross_ns_ratio | float | Fraction of edges crossing namespace boundaries |
-
-### v2/mathlib_summary.json
-
-Top-level keys: `snapshot` (commit, date, Lean version), `declaration_graph`, `module_graph`, `namespace_graph_k2` (node/edge counts, modularity, NMI, DAG depth, power-law exponents), `edge_decompositions` (proof-only/statement-only ratios), `kind_distribution`.
+| in_cycle | bool | In a strongly connected component (6,055 of 10,097) |
+| scc_id | int | SCC identifier (-1 if acyclic) |
 
 ## Methodology
 
-- **Extraction**: lean4export (nodes) + lean-training-data (edges) + importGraph (module graph) + jixia (declaration metadata)
-- **Deduplication**: by name, 317,655 to 308,129 rows (9,526 `@[to_additive]` mirrors removed)
-- **Self-loops**: 4,755 constructor self-references filtered from graph construction
+- **Extraction**: lean4export (nodes) + lean-training-data (edges) + importGraph (module graph) + jixia (metadata)
+- **Deduplication**: by name, 317,655 to 308,129 rows (9,526 `@[to_additive]` mirrors)
+- **Self-loops**: 4,755 constructor self-references filtered
 - **PageRank**: alpha=0.85, max_iter=100, tol=1e-6
-- **Betweenness**: declaration k=500, namespace k=300, module exact; all with seed=42
-- **Communities**: Louvain (python-louvain), resolution=1.0, random_state=42, on undirected projection
-- **DAG layers**: Kahn's algorithm; 5,732 declaration nodes in cycles assigned layer=-1; namespace graph condensed via SCC
+- **Betweenness**: declaration k=500, namespace k=300, module exact; seed=42
+- **Communities**: Louvain, resolution=1.0, random_state=42, undirected projection
+- **DAG layers**: Kahn's algorithm; cycle nodes get layer=-1; namespace graph condensed via SCC
+- **Namespace cycles**: 6,055 of 10,097 namespaces in 38 SCCs (largest: 5,899 nodes)
 
 ## License