  If quenched fast enough, a liquid is able to avoid crystallization and will
remain in a metastable supercooled state down to the glass transition, with an
important increase in viscosity upon further cooling. There are important
differences in the way liquids relax as they approach the glass transition,
rapid or slow variation in dynamic quantities under moderate temperature
changes, and a simple means to quantify such variations is provided by the
concept of "fragility". Here, we report molecular dynamics simulations of a
typical network-forming glass, Ge-Se, and find that the relaxation behaviour of
the supercooled liquid is strongly correlated to the variation of rigidity with
temperature and the spatial distribution of the corresponding topological
constraints which, ultimately connect to fragility minima. This permits
extending the fragility concept to aspects of topology/rigidity, and to the
degree of homogeneity of the atomic-sale interactions for a variety of
structural glasses.
