Before revision:  The clarified principal component reveals that (a)the expected first meeting time is almost dominated by n/(1+d_{\rm std}^2/d_{\rm avg}^2) and (b)the expected first meeting time is independent of the starting nodes of random walkers  where n is the number of nodes of the graph. d_{\rm avg} and d_{\rm std} are the mean and the standard deviation of weighted node degrees, respectively.
After revision:  The clarified principal component reveals that (a)the expected first meeting time is almost dominated by n/(1+d_{\rm std}^2/d_{\rm avg}^2) and (b)the expected first meeting time is independent of the starting nodes of random walkers , where n is the number of nodes of the graph. d_{\rm avg} and d_{\rm std} are the mean and the standard deviation of weighted node degrees, respectively.