  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.
