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This article constructs the residual network after some regions were damagedand detached from the original crystal network. This residual crystal networksimulates the situation where parts of a computer system or power system failedafter been attacked in real life. Furthermore, we assign multiple weightfactors to the edges in the network, exhibiting mixed weight growth. By usingthe symmetry and self-similarity of the network structure, the analyticalexpression for the average trapping time and the average weighted shortest pathon this network are solved, and the numerical results are given by taking theresidual hexagonal crystal network as an example. By analyzing the network andstudying the topological properties, we show the robustness of the networkstructure and find the residual network is more efficient for communicationbetween nodes.

Scaling of average trapping time and average weighted shortest path on a residual multi-weighted crystal network