| --- |
| 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 | |
|
|
| ### Enriched Data (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 (source file) metrics | |
| | `v2/mathlib_namespaces_k2.csv` | 10,097 | 9 | Per-namespace (depth-2) 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_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 |
|
|
