Before revision:  According to the revealed effect of graph structures, the variance of  coefficient d_{\rm std}/d_{\rm avg}(degree heterogeneity) for weighted degrees facilitates quicker the meeting of random walkers.
After revision:  According to the revealed effect of graph structures, the variance of coefficient d_{\rm std}/d_{\rm avg}(degree heterogeneity) for weighted degrees facilitates the meeting of random walkers.