The Measures of Rank or Status: A Reformulation and Reinterpretation

摘要

This article investigates methods in social network analysis to identify the most important or the most prominent actors in a social network by ranking them appropriately. Although much has been done since Seeley's (194926. Seeley , J. R. ( 1949 ). The net of reciprocal influence: A problem in treating sociometric data . Canadian Journal of Psychology , 3 , 234 - 240 .[CrossRef]View all references) seminal work, several questions remain: How does scaling an adjacency matrix of a social network affect its eigenvalues and their corresponding eigenvectors? How can the differences between the left and the right eigenvectors be reconciled? Do both depict the two sides of the same coin? Can they be “merged” objectively to yield a single eigenvector, and how? Under what conditions does an adjacency matrix characterize, as a first-order approximation, the dynamics of its corresponding social network? Most importantly, how can a general dynamic model be derived to make clear the interrelationships of existing models?In answering these questions, we derive a general model for the evolving rank (which we define as a general measure of prominence) of a (fixed) set of actors in a social network from a system of nonlinear equations; show that, under a rank equivalence condition, an adjacency matrix characterizes the dynamics of its corresponding social network as a first-order approximation; put some existing models within a single framework; and give a solution to the vexing problem of specifying the reference values of the rank.View full textDownload full textKeywordsBoolean matrix, equivalence condition, matrix scaling, measures, models, rank of the receiver, rank of the sender, rank prestigeRelated var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/0022250X.2011.556763