  This article constructs the residual network after some regions were damaged
and detached from the original crystal network. This residual crystal network
simulates the situation where parts of a computer system or power system failed
after been attacked in real life. Furthermore, we assign multiple weight
factors to the edges in the network, exhibiting mixed weight growth. By using
the symmetry and self-similarity of the network structure, the analytical
expression for the average trapping time and the average weighted shortest path
on this network are solved, and the numerical results are given by taking the
residual hexagonal crystal network as an example. By analyzing the network and
studying the topological properties, we show the robustness of the network
structure and find the residual network is more efficient for communication
between nodes.
