  Using information of the ground state topology and the damage spreading
technique we show a Griffiths-like phase is present in the three-dimensional
$\pm J$ Edwards-Anderson spin glass model. With spin-flipping dynamics damage
spreads for temperatures larger than $T_{\mathrm{g}}$, the glass transition
temperature. With spin-orienting dynamics and for temperatures in
$T_{\mathrm{g}} < T < T_{\mathrm{d}}$, damage spreads over a finite region of
the system, composed of finite clusters of ferromagnetic character.
$T_{\mathrm{d}}$ is the spin-orienting damage critical temperature, which is of
the same order as the critical temperature of the ferromagnetic Ising model,
$T_{\mathrm{c}}$. The present results allow us to identify the clusters which
originate the Griffiths-like phase in the present model.
