Dimension

Indicators

Description

Variety

Number of referenced disciplines

N

Balance

Shannon diversity normalized by variety

$-\frac{1}{\ln \left(n\right)}{\displaystyle {\sum }_i{p}_i\ln p_i}$ where n is the number of NSF specialty, p_i is the proportion of references in NSF specialty i

Reverse Gini coefficient

$1-\frac{{{\displaystyle \sum }}^{\text{}}\left(2i-n-1\right)x_i}{n{\displaystyle \sum x_i}}$ where i is the index, x_i is the number of references to the i-th NSF specialty, and specialties are sorted by x_i in non-decreasing order.

Disparity

Average dissimilarity between referenced disciplines

$\frac{1}{n\left(n-1\right)}{\displaystyle {\sum }_{i\ne j}{d}_{ij}}$ where d_ij is the dissimilarity between NSF specialty i and j. Specifically, d_ij = 1 − s_ij, where s_ij is the cosine similarity between NSF specialty i and j based on their co-citation matrix.