Retraction Note: Modified box dimension and average weighted receiving time on the weighted fractal networks.

This paper has been retracted.

The entire mean weighted first-passage time on a family of weighted treelike networks.

In this paper, we consider the entire mean weighted first-passage time (EMWFPT) with random walks on a family of weighted treelike networks. The EMWFPT on weighted networks is proposed for the first time in the literatures. The dominating terms of the EMWFPT obtained by the following two methods are coincident.

Modified box dimension and average weighted receiving time on the weighted fractal networks.

In this paper a family of weighted fractal networks, in which the weights of edges have been assigned to different values with certain scale, are studied. For the case of the weighted fractal networks the definition of modified box dimension is introduced, and a rigorous proof for its existence is given. Then, the modified box dimension depending on the weighted factor and the number of copies is deduced.