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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