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Datasets:
mgmacleod
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wikidata1

Tasks:
Graph Machine Learning
Feature Extraction
Modalities:
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Formats:
csv
Languages:
English
Size:
< 1K
Tags:
wikipedia
graph-theory
network-analysis
basins-of-attraction
phase-transition
knowledge-graph
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Polars
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metadata 
license: cc-by-sa-4.0
task_categories:
  - graph-ml
  - feature-extraction
language:
  - en
tags:
  - wikipedia
  - graph-theory
  - network-analysis
  - basins-of-attraction
  - phase-transition
  - knowledge-graph
size_categories:
  - 10M<n<100M

Wikipedia N-Link Basins

A novel graph-theoretic analysis of Wikipedia's internal link structure, revealing deterministic "basins of attraction" under N-link traversal rules.

Dataset Description

This dataset demonstrates that Wikipedia's 17.9 million pages partition into coherent regions when following a simple rule: from any page, always follow the Nth link. Every page eventually reaches a cycle, and pages sharing the same terminal cycle form a basin of attraction.

Key Discovery: Phase Transition at N=5

At N=5, Wikipedia's link graph exhibits a dramatic phase transition where basin sizes peak, then collapse by 10-1000× at higher N values.

Dataset Structure

Configurations

default (Recommended, 1.8 GB)

Full reproducibility package - everything needed to regenerate all reports, figures, and visualizations.

multiplex (125 MB)

Cross-N analysis results only. Sufficient for exploring findings.

source (1.6 GB)

Raw link sequences for computing any N value from scratch.

analysis (44 MB)

Per-N basin assignments and 3D geometry data for visualizations.

Data Files

Split File Rows Description
source nlink_sequences.parquet 18.0M Link sequences per page (up to 3873 links)
source pages.parquet 64.7M Page ID to title mapping
multiplex multiplex_basin_assignments.parquet 2.1M Basin membership per page per N
multiplex tunnel_nodes.parquet 2.1M Pages that switch basins across N
multiplex multiplex_edges.parquet 9.7M Multiplex graph edges
analysis branches_n={3-10}_*_assignments.parquet varies Per-N basin assignments
analysis basin_pointcloud_*.parquet varies 3D geometry for visualizations

Data Fields

multiplex_basin_assignments

  • page_id (int64): Wikipedia page identifier
  • N (int8): N-link rule value (3-10)
  • cycle_key (string): Raw cycle identifier for this N
  • canonical_cycle_id (string): Normalized basin identifier (stable across N)
  • entry_id (int64): Page ID of entry point into terminal cycle
  • depth (int32): Distance from terminal cycle

tunnel_nodes

  • page_id (int64): Wikipedia page identifier
  • basin_at_N3 through basin_at_N10 (string): Basin assignment at each N value (null if page not in any basin at that N)
  • n_distinct_basins (int8): Number of unique basins this page belongs to across N values
  • is_tunnel_node (bool): True if page switches basins across N values

Dataset Statistics

Metric Value
Total Wikipedia pages 17,972,018
Pages in analysis 2,079,289
Basins tracked 9 major cycles
Tunnel nodes 9,018 (0.45%)
N range 3-10

Basin Sizes at N=5 (Phase Transition Peak)

Basin Pages
Massachusetts ↔ Gulf_of_Maine 1,009,471
Sea_salt ↔ Seawater 265,896
Mountain ↔ Hill 188,968
Autumn ↔ Summer 162,689
Kingdom_(biology) ↔ Animal 112,805

Usage 

from datasets import load_dataset

# Load multiplex configuration
ds = load_dataset("your-username/wikipedia-nlink-basins", "multiplex")

# Access basin assignments
basins = ds['train'].to_pandas()
n5_basins = basins[basins.N == 5]

# Find tunnel nodes
tunnels = ds['tunnel_nodes'].to_pandas()
tunnel_pages = tunnels[tunnels.is_tunnel_node]
print(f"Pages that switch basins: {len(tunnel_pages):,}")

Curation Rationale

This dataset was created to:

  1. Validate N-Link Rule Theory - Prove that finite graphs partition into disjoint basins under deterministic rules
  2. Discover phase transitions - Identify critical N values where structure changes dramatically
  3. Enable graph ML research - Provide labeled basin memberships for GNN experiments
  4. Support knowledge graph analysis - Study Wikipedia's semantic structure through graph dynamics

Source Data

Wikipedia Dump: enwiki-20251220 (English Wikipedia, December 2025)

Processing Pipeline:

  1. Extract internal links from article prose (excluding navigation, infoboxes)
  2. Resolve redirects to canonical page IDs
  3. Store ordered link sequences per page
  4. Trace N-link paths to terminal cycles
  5. Assign basin membership

Considerations for Using the Data

Social Impact

This dataset reveals structural properties of Wikipedia's knowledge organization. Findings could inform:

  • Information navigation and search
  • Knowledge graph construction
  • Understanding editorial link patterns

Limitations

  • English Wikipedia only (cross-language validation pending)
  • Link structure reflects December 2025 snapshot
  • Basin analysis covers 9 major cycles (not exhaustive)

Bias

Wikipedia's link structure reflects editorial decisions and systemic biases present in the encyclopedia.

Additional Information

Licensing

CC BY-SA 4.0 (same as Wikipedia source)

Citation 

@dataset{wikipedia_nlink_basins_2026,
  title={Wikipedia N-Link Basins: Phase Transitions in Knowledge Graph Structure},
  year={2026},
  publisher={Hugging Face Datasets},
  howpublished={\url{https://huggingface.co/datasets/wikipedia-nlink-basins}}
}

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