It is shown that a simple renormalization allows nearly all B(E2:2(1)+ --> 0(1)+) values to be encompassed in a tight correlation envelope when plotted against N(p)N(n). Through such a valence correlation scheme, ''deviant'' nuclei are highlighted, and it is concluded that B (E2:2(1)+ --> 0(1)+) values alone can provide signatures, not only of quadrupole collectivity, but also of axial asymmetry, hexadecapole shapes, shape coexistence, saturation of collectivity, shell structure, and the evolution of shell gaps. Moreover, combined with E(4(1)+)/E(2(1)+) ratios, B(E2:2(1)+ --> 0(1)+) values provide a simple new signature to distinguish the two principal classes of nuclear phase transitions.