The Logarithmic Eigenfactor: Solving the Problems with the Normalized Eigenfactor

Since the introduction of the Normalized Eigenfactor as a journal influence factor in 2009,there has been little research into potential problems with this measure.In order to explore and resolve drawbacks associated with the Normalized Eigenfactor,this paper begins by proving that the discriminability realized by this method can be improved upon.By using the JCR2016 mathematics journals as an example,an analysis from the perspective of the discriminative degree and data distribution is performed to compare the Eigenfactor Score with that of the Normalized Eigenfactor.This is done using the Median Maximum Value Ratio,High Score Ratio,Low Score Ratio,Passing Rate,Discrete Coefficient,HHI and Jarque-Bera Test values.The results of the study show that the Normalized Eigenfactor had little effect on the discrimination and data distribution over the Eigenfactor.As such,the published accuracy of Eigenfactor Scores is misleading in claims that the Normalized Eigenfactor can improve the discriminating degree.In reality,it only becomes significant when magnifying the mean value of the Eigenfactor Score by more than 100 times.The Normalized Eigenfactor is a nonlinear transformation,and it will slightly degrade the information captured by the Eigenfactor Score.When the Normalized Eigenfactor is converted,the numerator is the journal’s Eigenfactor Score,and the denominator is derived from other journals’Eigenfactors;therefore,the scale of the measurement is not fixed and is at odds with the basic principle of measurement.Furthermore,the divergence between indicator values and evaluation attributes of the Normalized Eigenfactor manifests as data distribution bias,a low Pass Rate,and low sub-area data congestion.On this basis,this paper proposes to replace the Normalized Eigenfactor with the Logarithmic Eigenfactor.