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Citation impacts revisited: how novel impact measures reflect interdisciplinarity and structural change at the local and global level

Citation networks have fed numerous works in scientific evaluation, science mapping (and more recently large-scale network studies) for decades. The variety of citation behavior across scientific fields is both a research topic in sociology of science, and a problem in scientific evaluation. Normalization, tantamount to a particular weighting of links in the citation network, is necessary for allowing across-field comparisons of citation scores and interdisciplinary studies. In addition to classical normalization which drastically reduces all variability factors altogether, two tracks of research have emerged in the recent years. One is the revival of iterative "influence measures". The second is the "citing-side" normalization, whose only purpose is to control for the main factor of variability, the inequality in citing propensity, letting other aspects play: knowledge export/imports and growth. When all variables are defined at the same field-level, two propositions are established: (a) the gross impact measure identifies with the product of relative growth rate, gross balance of citation exchanges, and relative number of references (b) the normalized impact identifies with the product of relative growth rate and normalized balance. At the science level, the variance of growth rate over domains is a proxy for change in the system, and the variance of balance a measure of inter-disciplinary dependences. This opens a new perspective, where the resulting variance of normalized impact, and a related measure, the sum of these variances proposed as a Change-Exchange Indicator, summarize important aspects of science structure and dynamism. Results based on a decade's data are discussed. The behavior of normalized impact according to scale changes is also briefly discussed.