Before revision:  and (b)the expected first meeting time is independent of the beginning nodes of multiple random walks where n is the number of nodes  . d_{\rm avg} and d_{\rm std} are the mean and  standard deviation of the weighted degree of each node , respectively. n and d_{\rm avg, and d_{\rm std} are related to the statistics of graph structures}  . According to the analysis result , the variance of coefficient for weighted degrees, d_{\rm std}/d_{\rm avg}(degree heterogeneity)
After revision:  and (b)the expected first meeting time is independent of the beginning nodes of multiple random walks where n is the number of nodes . d_{\rm avg} and d_{\rm std} are the mean and standard deviation of the weighted degree of each node , respectively. n and d_{\rm avg, and d_{\rm std} are related to the statistics of graph structures} The characteristics (a) is useful to understand the effect of the graph structure on the first meeting time . According to the analysis result , the variance of coefficient for weighted degrees, d_{\rm std}/d_{\rm avg}(degree heterogeneity)