Established Clustering Procedures for Network Analysis (0806.4168v1)

Abstract: In light of the burgeoning interest in network analysis in the new millenium, we bring to the attention of contemporary network theorists, a two-stage double-standarization and hierarchical clustering (single-linkage-like) procedure devised in 1974. In its many applications over the next decade--primarily to the migration flows between geographic subdivisions within nations--the presence was often revealed of hubs''. These are, typically,cosmopolitan/non-provincial'' areas--such as the French capital, Paris--which send and receive people relatively broadly across their respective nations. Additionally, this two-stage procedure--which ``might very well be the most successful application of cluster analysis'' (R. C. Dubes)--has detected many (physically or socially) isolated groups (regions) of areas, such as those forming the southern islands, Shikoku and Kyushu, of Japan, the Italian islands of Sardinia and Sicily, and the New England region of the United States. Further, we discuss a (complementary) approach developed in 1976, involving the application of the max-flow/min-cut theorem to raw/non-standardized flows.