  In this study we are interested mainly in investigating the relations between
two graph irregularity measures which are widely used for structural
irregularity characterization of connected graphs. Our study is focused on the
comparison and evaluation of the discriminatory ability of irregularity
measures called degree deviation S(G) and degree variance Var(G). We establish
various upper bounds for irregularity measures S(G) and Var(G). It is shown
that the Nikiforov's inequality which is valid for connected graphs can be
sharpened in the form of Var(G) < S(G)/2. Among others it is verified that if G
is a bidegreed graph then the discrimination ability of S(G) and Var(G) is
considered to be completely equivalent.
