README.md

metadata

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 (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

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
• Edges: lean-training-data premises
• Module graph: importGraph
• Enrichment: NetworkX (PageRank, betweenness, Louvain, DAG layers)
• Code: MathlibGraph on GitHub

Citation

Part of the MathlibGraph project — network analysis of formalized mathematics.

License

Apache 2.0