algo-net-centrality

# Network Centrality Metrics ## Overview Centrality measures quantify node importance in a network. Four classical metrics: degree (connections), betweenness (bridge role), closeness (proximity), eigenvector (connection quality). Each captures a different aspect of importance. Complexity ranges from O(V+E) for degree to O(V×E) for betweenness. ## When to Use **Trigger conditions:** - Identifying key influencers or critical nodes in social/organizational networks - Analyzing network vulnerabilities (which node failure causes most damage) - Comparing node importance across different dimensions **When NOT to use:** - For group/community detection (use community detection algorithms) - For information spread modeling (use epidemic models) ## Algorithm ``` IRON LAW: Different Centrality Metrics Answer DIFFERENT Questions - Degree: Who has the most connections? (popularity) - Betweenness: Who bridges communities? (brokerage) - Closeness: Who can reach everyone fastest? (efficiency) - Eigenvector: Who is connected to important people? (prestige) Using the WRONG metric answers the WRONG question. Choose based on what "important" means in your context. ``` ### Phase 1: Input Validation Build network graph from edge list or adjacency matrix. Determine: directed vs undirected, weighted vs unweighted, connected vs disconnected. **Gate:** Graph is well-formed, largest connected component identified. ### Phase 2: Core Algorithm 1. **Degree centrality:** C_D(v) = deg(v) / (N-1). O(...