Petri net is a well-known
bipartite graph theory to model and analyze discrete event systems. The properties of Petri net can be classified into two types, i.e.,
behavioral property and
structural property. Many behavioral properties are investigated in association with the
markings of Petri nets. On the other hand, the structural properties are just considered based on the Petri net structure without markings. In this meaning, Petri net has been classified to
normal, cycle and
parallel structures according to its homogenous state matrix equation. As Petri net is a bipartite graph, its structure can be transformed into a
directed graph and the
Mason's theorem can be applied to know the properties of the original net. In this paper, we discuss the relationship between Petri net structure and directed graph, and describe some results for the normal and cycle structures of Petri nets. Furthermore, several useful concepts, for example,
transitive graph and
transitive matrix are also defined here, and its
characteristic polynomial and
characteristic equation are used to find out the cycle structures.
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