README.md

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

Module and Namespace Graphs (v2)

File	Rows	Description
v2/mathlib_module_nodes.csv	7,564	Module (source file) list with decl_count
v2/mathlib_module_edges.csv	20,881	Module import edges (source, target)
v2/mathlib_namespace_nodes_k2.csv	10,097	Depth-2 namespace list with decl_count
v2/mathlib_namespace_edges_k2.csv	332,081	Namespace edges with weight (aggregated from declaration edges)

Enriched Metrics (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 precomputed metrics
v2/mathlib_namespaces_k2.csv	10,097	9	Per-namespace precomputed 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_module_nodes.csv

Column	Type	Description
module	str	Dotted module name (e.g., Mathlib.Algebra.Group.Defs)
decl_count	int	Number of declarations defined in this module

v2/mathlib_module_edges.csv

Column	Type	Description
source	str	Importing module
target	str	Imported module

v2/mathlib_namespace_nodes_k2.csv

Column	Type	Description
namespace	str	Depth-2 namespace (e.g., Mathlib.Algebra)
decl_count	int	Declarations in this namespace

v2/mathlib_namespace_edges_k2.csv

Column	Type	Description
source	str	Source namespace
target	str	Target namespace
weight	int	Number of declaration-level edges between these namespaces

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