  For unramified reductive groups, we determine the connected components of
affine Deligne-Lusztig varieties in the partial affine flag varieties. Based on
the work of Hamacher-Kim and Zhou, this result allows us to verify, in the
unramified group case, the He-Rapoport axioms, the ``almost product structure"
of Newton strata, and the precise description of mod $p$ isogeny classes
predicted by the Langlands-Rapoport conjecture, for the Kisin-Pappas integral
models of Shimura varieties of Hodge type with parahoric level structure.
