A two-stage algorithm for extracting the multiscale backbone of complex weighted networks

The central problem of concern to Serrano, Boguña and Vespignani [1] can be effectively and elegantly addressed using a well-established two-stage algorithm that has been applied to internal migration flows for numerous nations and several other forms of ”transaction flow data” [2, 3, 4]. In the first stage, the N row and N column sums of the N × N matrix of weighted, directed network flows (fij) are alternately scaled to all equal 1, iteratively, until sufficient convergence to a doubly-stochastic table is attained. So doing serves as a control for multiscale effects. (This procedure–convergent under broad conditions [5]–leaves the cross-product ratios fijfkl filfkj [measures of association] invariant,