Network Community Clustering Using k-medoids Algorithm

Network community clustering is a technique that partitions network nodes into distinct groups where intra-group connections are dense while inter-group connections are sparse. The k-medoids algorithm is frequently employed for such problems due to its robustness and interpretability. Algorithm Principles k-medoids is an enhanced version of k-means that selects actual existing nodes (medoids) as cluster centers instead of calculating mean points. This characteristic makes it particularly suitable for network data since mean points may lack practical meaning in network space. The algorithm consists of four phases: Initialization Phase: Randomly select k nodes as initial medoids Assignment Phase: Assign each node to the cluster of its nearest medoid Update Phase: Within each cluster, reselect the node that minimizes the total distance as the new medoid Iteration Phase: Repeat assignment and update steps until medoids stabilize The key innovation involves using a distance matrix (e.g., based on shortest-path distances between nodes) instead of Euclidean distance, enabling the algorithm to adapt to network topology. Compared to k-means, k-medoids demonstrates lower sensitivity to outliers but requires higher computational complexity. Implementation Guidelines When implementing network clustering, three critical aspects require attention: Distance matrix construction should reflect network characteristics, commonly using shortest-path distances or Jaccard similarity transformations Initial medoid selection significantly impacts result quality - consider multiple random initializations with optimal solution selection Termination conditions should combine maximum iteration limits and minimum improvement thresholds for robust convergence This algorithm works best for small to medium-scale networks (up to 10^4 nodes) and achieves optimal performance on networks with clearly defined community structures. Practical applications should evaluate clustering quality using modularity metrics and validate results through visualization tools. Code implementation typically involves creating a distance matrix using networkx shortest_path_length() function, implementing medoid update logic with numpy argmin() operations, and incorporating convergence checks with tolerance parameters.