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

# MathlibGraph: Mathlib Dependency Graph Dataset

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. Lean version: `v4.28.0-rc1`.

## Files

### Core data (v1)

| File | Rows | Description |
|------|------|-------------|
| `mathlib_nodes.csv` | 317,655 (308,129 unique) | Mathlib declarations (name, kind, module) |
| `mathlib_edges.csv` | 8,436,366 | Mathlib dependencies (source, target, is_explicit, is_simplifier) |
| `nodes.csv` | 633,364 | Full environment (Lean + Std + Mathlib) |
| `edges.csv` | 10,889,011 | Full environment edges |
| `mechanisms.ndjson` | — | Lean language mechanism extractions |
| `tactic_usage.ndjson` | — | Tactic usage profiles |

### Enriched data (v2)

| File | Rows | Description |
|------|------|-------------|
| `v2/mathlib_nodes_enriched.csv` | 308,129 | Deduplicated nodes with 8 precomputed metric columns |
| `v2/mathlib_modules.csv` | 7,564 | Per-module (source file) metrics |
| `v2/mathlib_namespaces_k2.csv` | 10,097 | Per-namespace (depth-2) metrics |
| `v2/mathlib_summary.json` | — | Headline statistics for all three graph levels |

> **Note:** `mathlib_nodes.csv` contains 9,526 duplicate name rows from `@[to_additive]` mirroring. The v2 enriched file is deduplicated to **308,129 unique declarations**.

## Statistics (308,129 unique Mathlib declarations)

| Kind | Count | % |
|------|-------|---|
| theorem | 251,642 | 79.2% |
| definition | 50,156 | 15.8% |
| abbrev | 6,784 | 2.1% |
| constructor | 4,755 | 1.5% |
| inductive | 3,813 | 1.2% |
| opaque | 499 | 0.2% |
| quotient | 3 | <0.1% |
| axiom | 3 | <0.1% |

## Quick Start

```python
from datasets import load_dataset

# Load enriched nodes (v2, deduplicated, with metrics)
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):,}")
# Declarations: 308,129, Edges: 8,436,366

# Top 10 by PageRank
print(nodes.nlargest(10, "pagerank")[["name", "kind", "in_degree", "pagerank"]])

# Load module-level data
modules = load_dataset("MathNetwork/MathlibGraph",
                       data_files="v2/mathlib_modules.csv", split="train").to_pandas()
print(f"Modules: {len(modules):,}")
```

## Schema

### mathlib_nodes.csv (v1)

| Column | Type | Description |
|--------|------|-------------|
| name | string | Fully qualified declaration name |
| kind | string | `theorem`, `definition`, `abbrev`, `inductive`, `constructor`, `opaque`, `axiom`, `quotient` |
| module | string | Parent namespace of the declaration |

### mathlib_edges.csv

| Column | Type | Description |
|--------|------|-------------|
| source | string | Dependent declaration |
| target | string | Dependency (premise) |
| is_explicit | bool | Appears in explicit arguments (25.8% of edges) |
| is_simplifier | bool | Used by simplifier |

### v2/mathlib_nodes_enriched.csv

All columns from `mathlib_nodes.csv` plus:

| Column | Type | Description |
|--------|------|-------------|
| namespace_depth2 | string | Depth-2 namespace (e.g., `Mathlib.Algebra`) |
| namespace_depth3 | string | Depth-3 namespace (e.g., `Mathlib.Algebra.Group`) |
| in_degree | int | Number of declarations that depend on this one |
| out_degree | int | Number of declarations this one depends on |
| pagerank | float | PageRank score (alpha=0.85) |
| betweenness | float | Betweenness centrality (sampled, k=500, seed=42) |
| community_id | int | Louvain community ID (resolution=1.0, seed=42) |
| dag_layer | int | Topological depth in DAG (-1 if in a cycle; 5,732 nodes) |

### v2/mathlib_modules.csv

One row per Mathlib source file (7,564 modules).

| Column | Type | Description |
|--------|------|-------------|
| module | string | Dotted module name (e.g., `Mathlib.Algebra.Group.Defs`) |
| decl_count | int | Declarations in this module (from jixia extraction, 235K coverage) |
| in_degree | int | Modules that import this module |
| out_degree | int | Modules this module 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 ID |
| cohesion | float | internal_edges / (internal + external) |
| import_utilization_median | float | Median fraction of imported declarations actually used |

### v2/mathlib_namespaces_k2.csv

One row per depth-2 namespace (10,097 namespaces).

| Column | Type | Description |
|--------|------|-------------|
| namespace | string | 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 in namespace graph |
| edge_weight_sum | int | Weighted degree (sum of declaration-level edges) |
| pagerank | float | PageRank (weighted, alpha=0.85) |
| betweenness | float | Betweenness centrality (k=300, seed=42, weighted) |
| community_id | int | Louvain community ID (weighted undirected) |
| cross_ns_ratio | float | Fraction of this namespace's edges that cross namespace boundaries |

### v2/mathlib_summary.json

Headline statistics including: snapshot metadata (commit, date, Lean version), declaration/module/namespace graph metrics (node/edge counts, modularity, NMI, DAG depth, power-law exponents), and edge decomposition ratios.

## Extraction Pipeline

- **Nodes**: [lean4export](https://github.com/leanprover/lean4export)
- **Edges**: [lean-training-data premises](https://github.com/kim-em/lean-training-data)
- **Module graph**: [importGraph](https://github.com/leanprover-community/importGraph)
- **Enrichment**: NetworkX (PageRank, betweenness, Louvain, DAG layers)
- **Code**: [MathlibGraph on GitHub](https://github.com/MathNetwork/MathlibGraph)

## Citation

Part of the [MathlibGraph](https://github.com/MathNetwork/MathlibGraph) project — network analysis of formalized mathematics.

## License

Apache 2.0