Abstract
In this paper, we mainly study two important properties of weighted Cayley networks depending on a weight factor r. The weight factor makes it more difficult to calculate the topological characteristics such as average weighted shortest path (AWSP) and average receiving time (ART) of the networks. We first calculate some basic network measurements such as average degree and average node strength. Then we derive the expression for AWSP and show that it stays bounded with network order growing (0<r<1) in the limit of large network order. At last, we focus on random walks and trapping issue on the networks. That is, we calculate the ART. In more detail: for 0<r<12, the ART grows with increasing size Nt as lnNt; for r=12, the ART grows with increasing size Nt as ln2Nt; for 12<r<1, the ART grows sublinearly with the network size Nt; for r=1, the ART grows linearly with the network size Nt.
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