$\mathbf{h_\alpha}$: An index to quantify an individual's scientific leadership

The $\alpha$ person is the dominant person in a group. We define the $\alpha$-author of a paper as the author of the paper with the highest $h$-index among all the coauthors, and an $\alpha$-paper of a scientist as a paper authored or coauthored by the scientist where he/she is the $\alpha$-author. For most but not all papers in the literature there is only one $\alpha$-author. We define the $h_\alpha$ index of a scientist as the number of papers in the $h$-core of the scientist (i.e. the set of papers that contribute to the $h$-index of the scientist) where this scientist is the $\alpha$-author. We also define the $h'_\alpha$ index of a scientist as the number of $\alpha$-papers of this scientist that have $\geq$ $h'_\alpha$ citations. $h_\alpha$ and $h'_\alpha$ contain similar information, while $h'_\alpha$ is conceptually more appealing it is harder to obtain from existing databases, hence of less current practical interest. We propose that the $h_\alpha$ and/or $h'_\alpha$ indices, or other variants discussed in the paper, are useful complements to the $h$-index of a scientist to quantify his/her scientific achievement, that rectify an inherent drawback of the $h$-index, its inability to distinguish between authors with different coauthorships patterns. A high $h$ index in conjunction with a high $h_\alpha/h$ ratio is a hallmark of scientific leadership.