Nuclear reaction rate ($lambda$) is a significant factor in the process of nucleosynthesis. A multi-layer directed-weighted nuclear reaction network in which the reaction rate as the weight, and neutron, proton, $^4$He and the remainder nuclei as the criterion for different reaction-layers is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase of the stellar temperature ($T_{9}$), the distribution of nuclear reaction rates on the $R$-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei on the $R$-layer in the region of $lambda = [1,2.5times10^{1}]$ have a more complicated out-going degree distribution than the one in the region of $lambda = [10^{11},10^{13}]$, and the number of involved nuclei at $T_{9} = 1$ is very different from the one at $T_{9} = 3$. The redundant nuclei in the region of $lambda = [1, 2.5times10^{1}]$ at $T_{9} = 3$ prefer $(gamma,p)$ and $({gamma,alpha})$ reactions to the ones at $T_{9}=1$, which produce nuclei around the $beta$ stable line. This work offers a novel way to the big-data analysis on nuclear reaction network at stellar temperatures.
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