  Previous work shows that the mean first-passage time (MFPT) for random walks
to a given hub node (node with maximum degree) in uncorrelated random
scale-free networks is closely related to the exponent $\gamma$ of power-law
degree distribution $P(k)\sim k^{-\gamma}$, which describes the extent of
heterogeneity of scale-free network structure. However, extensive empirical
research indicates that real networked systems also display ubiquitous degree
correlations. In this paper, we address the trapping issue on the Koch
networks, which is a special random walk with one trap fixed at a hub node. The
Koch networks are power-law with the characteristic exponent $\gamma$ in the
range between 2 and 3, they are either assortative or disassortative. We
calculate exactly the MFPT that is the average of first-passage time from all
other nodes to the trap. The obtained explicit solution shows that in large
networks the MFPT varies lineally with node number $N$, which is obviously
independent of $\gamma$ and is sharp contrast to the scaling behavior of MFPT
observed for uncorrelated random scale-free networks, where $\gamma$ influences
qualitatively the MFPT of trapping problem.
