  We study the interplay between disorder and topology for the localized edge
states of light in topological zigzag arrays of resonant dielectric
nanoparticles. We characterize topological properties by the winding number
that depends on both zigzag angle and spacing between nanoparticles in the
array. For equal-spacing arrays, the system may have two values of the winding
number $\nu=0$ or $1$, and it demonstrates localization at the edges even in
the presence of disorder, being consistent with experimental observations for
finite-length nanodisk structures. For staggered-spacing arrays, the system
possesses richer topological phases characterized by the winding numbers
$\nu=0$, $1$ or $2$, which depend on the averaged zigzag angle and disorder
strength. In a sharp contrast to the equal-spacing zigzag arrays,
staggered-spacing arrays reveal two types of topological phase transitions
induced by the angle disorder, (i) $\nu = 0 \leftrightarrow \nu = 1$ and (ii)
$\nu = 1 \leftrightarrow \nu = 2$. More importantly, the spectrum of
staggered-spacing arrays may remain gapped even in the case of a strong
disorder.
