Let Γ(G) be a set of all simple graphs of order n and size m, without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ … ≥ dn > 0. A graph G is regular if and only if d1 = d2 = … = dn . Each mapping Irr: Γ(G) ›→ [0, +∞) with the property Irr(G) = 0 if and only if G is regular, is referred to as irregularity measure of graph. In this paper we introduce some new irregularity measures and inequalities that establish relations between them.