Wikipedia Administrator Voting Network Analysis

Wikipedia's Request for Adminship (RfA) is the process by which volunteer editors are elected to administrator roles, giving them tools to protect pages, block users, and delete content. Each election generates a structured vote record: who voted for whom.

This study treats the entire Wikipedia voting history (foundation to January 2008) as a directed social network and applies network science tools to uncover the hidden structure: who wields disproportionate influence, how voter blocs form, and how decentralised or centralised the governance process actually is.

• Network ingestion and construction using NetworkX from the raw edge list.
• Topological characterisation: node/edge counts, average degree, shortest paths, density, and diameter of the Giant Connected Component (GCC).
• Centrality measures: degree, betweenness, closeness, and eigenvector centrality to rank nodes by influence, bridge role, and information spread.
• Clustering analysis: assortativity coefficient, clustering coefficient distribution, and triangle counting to understand cohesion.
• Community detection: Girvan-Newman modularity decomposition and Louvain iterative community optimisation applied to the GCC.
• Network visualisation: Gephi with Fruchterman-Reingold force-directed layout; nodes coloured by community.

A density of 0.004 confirms the network is sparse: each voter engaged with a small fraction of all nominees, as expected in a governance process. The GCC diameter of 7 implies the "six degrees of separation" principle holds here too; any two participants are reachable within seven hops.

Five nodes dominate across all centrality measures: degree, betweenness, closeness, and eigenvector. These are the individuals most connected, most bridging, and most influential in the voting network.

Node 2565 alone is connected to approximately 1,065 voters, roughly 15% of all participants. The other four spotlight nodes each link to 700+ votes. The majority of nodes have betweenness centrality below 0.01, confirming the network's sparse bridge structure.

• Assortativity coefficient of −0.083 indicates weak disassortative mixing: highly-connected voters tend to link to less-connected nominees rather than to each other.
• The average clustering coefficient is 0.14, low compared to typical social networks, consistent with a governance process rather than a friendship network.
• About 200 nodes have a clustering coefficient of 1.0 (small, tight cliques), but most nodes sit in sparse neighbourhoods.
• 608,389 unique triangles exist across the network; the median triangles-per-node is just 1 against a mean of ~256. A handful of high-degree nodes drive that average upward.
• This heavy-tailed distribution is a hallmark of power-law social networks: a few hubs are deeply embedded in many overlapping cliques while most participants have minimal interconnection.

Both the Girvan-Newman algorithm (modularity-based edge removal) and the Louvain method (iterative modularity maximisation) were applied to the GCC. The two approaches converged on a consistent community partition, validating structural robustness of the clusters.

Communities likely reflect shared editorial interests, topic areas, or interaction history, though without node-level data these hypotheses can't be confirmed directly. Importantly, communities that form large cohesive blocs can exert collective influence on adminship outcomes, raising questions about bias and representativeness in the RfA process.

• The network is sparse and decentralised overall, but five "superconnector" nodes concentrate disproportionate influence.
• Node 2565 is the single most influential participant, reaching ~15% of all voters through direct connections.
• Low average clustering (0.14) suggests voting decisions are made independently rather than in tightly-knit peer groups, which is a good sign for governance integrity.
• The triangle count skew reveals that influence hubs participate in dense local clusters while the majority of voters remain loosely integrated.
• Community structure exists and persists across two independent detection algorithms, indicating real sub-groups with shared voting behaviour.
• "Small world" properties hold: an average path length of 3.2 means information or campaigning can reach the whole network through just a few hops.

• Enriching nodes with edit history, topic specialisation, and tenure could reveal why communities form and whether voting blocs introduce systematic biases.
• Temporal analysis (year-by-year snapshots) would show whether network centrality became more or less concentrated as Wikipedia matured.
• Comparing English Wikipedia with other language editions could expose cultural differences in governance structure.
• Anomaly detection on voting patterns could flag coordinated bloc voting or sockpuppet activity for Wikipedia's trust and safety teams.
• These network analysis methods are directly transferable to other online governance networks (Reddit moderator elections, DAO voting, etc.).