Abstract: This study introduces transition vectors based on place transitive matrix derived from graph theory, to study the structure of Petri nets using structure theoretical results that exists in Petri net theory. It has been established that transition vectors provide a simplified and more adequate approach than transitive matrix towards the structural analysis of PN. Some structural classes of Petri nets have been decided and basic concepts about the structure of Petri net have been derived through novel idea of transition vectors. Firstly new representation of place transitive matrix has been introduced for acyclic Petri nets. Secondly Petri net structure has been analyzed and an algorithm to find a directed cycle has been presented with a simplified representation, using transition vectors. Thirdly transition vectors have efficiently been used to identify the particular structures of Petri nets. Finally, useful concepts relevant to the structure of Petri nets have been derived.