README.md

---
license: apache-2.0
task_categories:
  - graph-ml
language:
  - en
tags:
  - mathematics
  - lean4
  - mathlib
  - dependency-graph
  - formal-verification
  - network-analysis
size_categories:
  - 100K<n<1M
---

# MathlibGraph: The Multinetwork of Mathlib

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.

## 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 |
| Louvain modularity | 0.478 | 0.610 | 0.270 |
| Synthesized edges | 74.2% | — | — |
| Cross-namespace edges | — | — | 85.8% |

## Files

### Raw Graph Data

| 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 |
| `mechanisms.ndjson` | — | Lean language mechanism extractions |
| `tactic_usage.ndjson` | — | Per-declaration tactic usage profiles |

### Module and Namespace 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) |

### Enriched Metrics (v2)

| 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 |

## Quick Start

```python
from datasets import load_dataset

nodes = load_dataset("MathNetwork/MathlibGraph",
                     data_files="v2/mathlib_nodes_enriched.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"]])
```

## 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/mathlib_module_edges.csv

| Column | Type | Description |
|--------|------|-------------|
| source | str | Importing module |
| target | str | Imported module |

### v2/mathlib_namespace_nodes_k2.csv

| Column | Type | Description |
|--------|------|-------------|
| namespace | str | Depth-2 namespace (e.g., `Mathlib.Algebra`) |
| decl_count | int | Declarations in this namespace |

### v2/mathlib_namespace_edges_k2.csv

| Column | Type | Description |
|--------|------|-------------|
| source | str | Source namespace |
| target | str | Target namespace |
| weight | int | Number of declaration-level edges between these namespaces |

### v2/mathlib_nodes_enriched.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 |

### v2/mathlib_modules.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) |
| 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) |
| 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 |

### v2/mathlib_namespaces_k2.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 |
| out_degree | int | Unweighted out-degree |
| edge_weight_sum | int | Sum of declaration-level 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 |
| 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`.

## 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
- **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

## License

Apache 2.0