  Here we show that a new class of glasses composed of heavy metal oxides
involving transition metals (V$_\text {2}$O$_\text{}$5-TeO$_\text{2}$), can
surprisingly be designed from very basic tools using topology and rigidity of
their underlying molecular networks. When investigated as a function of
composition, such glasses display abrupt changes in network packing and
enthalpy of relaxation at Tg, underscoring presence of flexible to rigid
elastic phase transitions. We find that these elastic phases are fully
consistent with polaronic nature of electronic conductivity at high
V$_\text{2}$O$_\text{5}$ content. Such observations have new implications for
designing electronic glasses which differ from the traditional amorphous
electrolytes having only mobile ions as charge carriers.
