On the gap of finite metric spaces of p-negative type

Let $(X\text{,}d)$ be a metric space of p-negative type. Recently I. Doust and A. Weston introduced a quantification of the p-negative type property, the so called gap $\mathrm{\Gamma }$ of X. This paper gives some formulas for the gap $\mathrm{\Gamma }$ of a finite metric space of strict p-negative type and applies them to evaluate $\mathrm{\Gamma }$ for some concrete finite metric spaces.