  Several studies have been reported in the literature about SN P system and
its variants. Often, the results provide universality of various variants and
the classes of languages that these variants generate and recognize. The state
of SN P system is its configuration. We refer to our previous result on
reachability of configuration as the {\it Fundamental state equation for SN P
system.} This paper provides a preliminary investigation on the behavioral and
structural properties of SN P system without delay that depend primarily to
this fundamental state equation. Also, we introduce the idea of configuration
graph $CG_{\Pi}$ of an SN P system $\Pi$ without delay to characterize
behavioral properties of $\Pi$ with respect to $CG_{\Pi}.$ The matrix $M_{\Pi}$
of an SN P system $\Pi$ without delay is used to characterize structural
properties of $\Pi.$
