This note tries to attempt a sketch of the history of spectral ranking-a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between entities. Albeit recently made famous by the ample press coverage of Google's PageRank algorithm, spectral ranking was devised more than fifty years ago, almost exactly in the same terms, and has been studied in psychology, social sciences, and choice theory. I will try to describe it in precise and modern mathematical terms, highlighting along the way the contributions given by previous scholars. This is is a work in progress with no claim of completeness. I have tried to collect evidence of spectral techniques in ranking from a number of sources, providing a unified mathematical framework that should make it possible to understand in a precise way the relationship between contributions. Reports of inaccuracies and missing references are more than welcome.
The history of the particular case h = h α is the subject of the excellent study of spectral ranking REF .
Spectral Ranking
Computer Science Physics