  Centrality-dependent measurements of hadron and jet cross section attenuation
in deep inelastic scattering on nuclei can shed new light on the physics of
final-state interactions in the nuclear matter, including the path-length
dependence of the in-medium parton shower formation and evolution. Recent
simulation studies have demonstrated the feasibility of experimental centrality
determination in $e$A reactions at the electron-ion collider via neutron
detection in the zero-degree calorimeter. Motivated by these results, we
present the first theoretical calculation of the production rate modification
for hadrons and jets in central and peripheral $e$Pb collisions. We find that
the variation in the suppression of inclusive jet cross section as a function
of centrality is less than a factor of two. In more differential measurements,
such as the distribution of hadrons versus the hadronization fraction $z_h$,
the difference can be enhanced up to an order of magnitude.
