Given an Artinian algebra $A$ over a field $k$, there are
several combinatorial objects associated to $A$. They are the
diagram $D_A$ as defined by Drozd and Kirichenko, the natural quiver $\Delta_A$
defined by Li (cf. Section 2), and a generalized version of
$k$-species $(A/r, r/r^2)$ with $r$ being the Jacobson radical of
$A$. When $A$ is splitting over the field $k$, the diagram $D_A$
and the well-known ext-quiver $\Gamma_A$ are the same. The main
objective of this paper is to investigate the relations among these
combinatorial objects and in turn to use these relations to give a
characterization of the algebra $A$.