algo-net-communitylisted

# Louvain Community Detection ## Overview Louvain algorithm detects communities by optimizing modularity — the fraction of edges within communities minus expected fraction if edges were random. A greedy, hierarchical algorithm that runs in O(n log n) for sparse graphs. Produces a hierarchy of communities at multiple resolutions. ## When to Use **Trigger conditions:** - Discovering natural groupings in social, organizational, or interaction networks - Segmenting users/customers by behavioral similarity - Analyzing modular structure of complex networks **When NOT to use:** - For overlapping communities (use DEMON or BigCLAM) - When communities are pre-defined and you're classifying nodes (use label propagation) ## Algorithm ``` IRON LAW: Modularity Has a RESOLUTION LIMIT Louvain optimizes modularity, which has a known resolution limit (Fortunato & Barthélemy, 2007): it cannot detect communities smaller than √(2E) where E = total edges. In large networks, small but real communities may be merged. Use multi-resolution methods or Leiden algorithm (improved Louvain) for better results. ``` ### Phase 1: Input Validation Build undirected weighted graph from interaction data. Edge weights represent interaction strength (frequency, duration, volume). **Gate:** Graph loaded, no isolated nodes (or decide how to handle them). ### Phase 2: Core Algorithm **Phase 1 — Local moves:** 1. Assign each node to its own community 2. For each node, compute modularity gain of moving to each