mgmacleod/wikidata1

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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