| --- |
| 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), 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 (weighted) | |
| | DAG depth | 83 | 154 | 7 (after SCC condensation) | |
| | Louvain modularity | 0.478 | 0.610 | 0.270 | |
| | Synthesized edges | 74.2% | — | — | |
| | In cycles | 5,732 nodes | 0 (DAG) | 6,055 nodes (38 SCCs) | |
|
|
| ## Files |
|
|
| ### Raw Data (v1) |
|
|
| | File | Rows | Description | |
| |------|------|-------------| |
| | `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 | |
|
|
| ### Three-Layer Graphs (v2) |
|
|
| Each layer has `nodes.csv`, `edges.csv`, and `metrics.csv`: |
|
|
| | 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 | |
|
|
| `v2/summary.json` contains headline statistics for all three levels. |
|
|
| ## Quick Start |
|
|
| ```python |
| from datasets import load_dataset |
| |
| # 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() |
| |
| # 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/declaration/nodes.csv |
|
|
| Deduplicated from `mathlib_nodes.csv` (317,655 to 308,129 rows; 9,526 `@[to_additive]` mirrors removed). |
|
|
| | Column | Type | Description | |
| |--------|------|-------------| |
| | 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/declaration/metrics.csv |
|
|
| All columns from `nodes.csv` plus: |
|
|
| | Column | Type | Description | |
| |--------|------|-------------| |
| | 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/module/nodes.csv |
|
|
| | Column | Type | Description | |
| |--------|------|-------------| |
| | module | str | Dotted module name (e.g., `Mathlib.Algebra.Group.Defs`) | |
| | decl_count | int | Declarations defined in this source file | |
| |
| ### v2/module/edges.csv |
| |
| | Column | Type | Description | |
| |--------|------|-------------| |
| | source | str | Importing module | |
| | target | str | Imported module | |
| |
| ### v2/module/metrics.csv |
| |
| | Column | Type | Description | |
| |--------|------|-------------| |
| | 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) | |
| | dag_layer | int | Topological depth in module DAG | |
| | 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/namespace/nodes.csv |
|
|
| | Column | Type | Description | |
| |--------|------|-------------| |
| | namespace | str | Depth-2 namespace (e.g., `Mathlib.Algebra`) | |
| | decl_count | int | Declarations in this namespace | |
| | 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 | 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 (weighted undirected) | |
| | cross_ns_ratio | float | Fraction of edges crossing namespace boundaries | |
| | 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 (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; 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 |
|
|
| Apache 2.0 |
|
|
