We present a Monte Carlo analysis of the recently introduced variability indices $\tau$ (Tompkins 1999) and $I$ (Zhang et al. 2000 & Torres et al. 2001) for $\gamma$-ray sources. We explore different variability criteria and prove that these two indices, despite the very different approaches used to compute them, are statistically correlated (5 to 7$\sigma$). This conclusion is maintained also for the subset of AGNs and high latitude ($|b|>10$ deg) sources, whereas the correlation is lowered for the low latitude ones, where the influence of the diffuse galactic emission background is strong.