metadata 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 (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
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
