An efficient entropy of sum approach for measuring diversity and interdisciplinarity

Rousseau and Mutz argued that the existing researches on diversity measure methods, such as the Rao-Stirling index, DIV, etc., have shortcomings, and urged colleagues to find a better framework for diversity measure. Based on Shannon entropy and entropy of degree vector sum, in this contribution a new diversity measure EDVS (Entropy of Degree Vectors Sum) is proposed, which meets all requirements of variety, balance and disparity, and can directly calculate the value of diversity from the observed sample data without calculating the joint probability distribution of two random variables, or mutual information. The empirical results show that: (1) the ranking of the EDVS measure has a higher Spearman correlation coefficient with DIV and DIV* than with Shannon entropy. (2) The EDVS ranking is more relevant with DIV* than with DIV. (3) The diversity of soft science journals is higher than that of hard science journals, which indicates that the interdisciplinary research of social sciences and humanities is more common than that of hard sciences such as sciences and engineering sciences. (4) Rao-Stirling index and DIV index are more sensitive to sample size. The computational complexity of the Rao-Stirling index and DIV index is O(n3), while the computational complexity of the EDVS index is O(n2). This provides the feasibility for analyzing high-dimension networks and large data sets. Results of verification on different types of data sets show that EDVS can not only effectively measure the diversity of disciplines in interdisciplinary research, but also effectively measure the diversity of other entities.