  We prove expectation and concentration results for the following random
variables on an Erd\H{o}s-R\'enyi random graph $\mathcal{G}\left(n,p\right)$ in
the sparsely connected regime $\log n + \log\log \log n \leq np < n^{1/10}$:
effective resistances, random walk hitting and commute times, the Kirchoff
index, cover cost, random target times, the mean hitting time and Kemeny's
constant. For the effective resistance between two vertices our concentration
result extends further to $np\geq c\log n, \; c>0$. To achieve these results,
we show that a strong connectedness property holds with high probability for
$\mathcal{G}(n,p)$ in this regime.
