  Excitations in (3+1)D topologically ordered phases have very rich structures.
(3+1)D topological phases support both point-like and string-like excitations,
and in particular the loop (closed string) excitations may admit knotted and
linked structures. In this work, we ask the question how different types of
topological excitations contribute to the entanglement entropy, or
alternatively, can we use the entanglement entropy to detect the structure of
excitations, and further obtain the information of the underlying topological
orders? We are mainly interested in (3+1)D topological orders that can be
realized in Dijkgraaf-Witten gauge theories, which are labeled by a finite
group $G$ and its group 4-cocycle $\omega\in\mathcal{H}^4[G;U(1)]$ up to group
automorphisms. We find that each topological excitation contributes a universal
constant $\ln d_i$ to the entanglement entropy, where $d_i$ is the quantum
dimension that depends on both the structure of the excitation and the data
$(G,\,\omega)$. The entanglement entropy of the excitations of the
linked/unlinked topology can capture different information of the DW theory
$(G,\,\omega)$. In particular, the entanglement entropy introduced by Hopf-link
loop excitations can distinguish certain group 4-cocycles $\omega$ from the
others.
