Nucleosynthesis is a complex process in astro-nuclear evolution. In this work, we construct a directed multi-layer nuclear reaction network using the substrate-product method from a thermonuclear reaction database, JINA REACLIB. The network contains four layers, namely $n$-, $p$-, $h$- and $r$, corresponding to the reaction types involved in neutrons, protons, $^4$He and the remainder, respectively. The degree values (i.e. numbers of reactions) for three layers of n-, p- and h- have a significant correlation with one another, and their topological structures exhibit a similar regularity. However, the $r$-layer has a more complex topological structure than others and has less correlation with the other three layers. A software package named `mfinder is employed to analyze the motif structure of the nuclear reaction network. We thus identify the most frequent reaction patterns of interconnections occurring among different nuclides. This work provides a novel approach to study the nuclear reaction network prevailing in the astrophysical context.
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