This topic discusses the principles and computational techniques for identifying cohesive substructures within social networks. Cliques, k-cores, and connected components are presented as mathematical constructs for quantifying local density and mutual connectivity, illustrating how tightly knit groups emerge from simple relational rules. The computational complexity of clique detection is analyzed in light of NP-hardness, with heuristic and recursive algorithms such as Bron–Kerbosch introduced as practical solutions for real-world datasets. 

The discussion extends to clustering coefficients and transitivity, showing how “the friends of my friends” phenomenon provides measurable evidence of social reinforcement and collective identity. The efficient computation of local and global clustering coefficients through matrix algebra and adjacency cube trace operations is highlighted as a scalable alternative to brute-force enumeration. Finally, modularity-based community detection algorithms—including Girvan–Newman and Louvain—are presented as frameworks for identifying large-scale social divisions. The topic concludes that clustering analysis is both a computational and interpretive act: one that reveals how local cohesion translates into global social architecture.

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