Scaling of average receiving time and average weighted shortest path on weighted-crystal network

In this paper, we focus on a network with even nodes named the weighted-crystal network, which is different from the regular iterative rules. By employing the self-similarity of the crystal network, we study and calculate the average receiving time (ART) and average weighted shortest path (AWSP) after dividing the network into n + 1 blocks. In particular, we pay attention to the hexagon crystal network in order to obtain exact results. The obtained scaled results show that ART grows linearly or sublinearly with the iterative and increases with the weight factor r. Meanwhile, the results of AWSP indicate that AWSP exhibits a sublinear dependence on the network order when r = 1. Otherwise, AWSP tends towards constants when 0 < r < 1.