For melts within the compatibility triangle anorthite–wollastonite–gehlenite (An–Wo–Geh) (CaAl2Si2O8–CaSiO3–Ca2Al2SiO7), the relationships between the chemical composition, the melt structure, and the rheological and thermodynamic properties are studied for each of the boundary lines, i.e. the An–Wo, Wo–Geh and Geh–An join. The influences of the degree of polymerization of the structural network and the amount of Al–O–Al linkages on the fragility and the configurational entropy of the melts are studied along the boundary lines. For the An–Wo join, the degree of polymerization dominates the responses of both fragility and configurational entropy to compositional variations. For the Wo–Geh and Geh–An joins, the amount of the Al–O–Al linkages dominates those responses. It is found that the depolymerization of the structural network and the formation of Al–O–Al linkages increase the fragility of the melt and the degree of structural disordering.