Abstract Non-configurationality is a linguistic property associated with free word order, discontinuous constituents, including NPs, and null anaphora of referential arguments. Quantitative metrics, based both on local networks (syntactic trees and word order within sentences) and on global networks (incorporating the relations within a whole treebank into a shared graph), can reveal correlations among these features. Using treebanks we focus on diachronic varieties of Ancient Greek and Latin, in which non-configurationality tapered off over time, leading to the largely configurational nature of the Romance languages and of Modern Greek. A property of global networks (density of their spectra around zero eigenvalues) measuring the regularity in word order is shown to be strengthened from classical to late varieties. Discontinuous NPs are traced by counting the words creating non-projectivity in dependency trees: these drop dramatically in late varieties. Finally, developments in the use of null referential direct objects are gauged by assessing the percentage of third-person personal pronouns among verb objects. All three features turn out to change over time due to the decay of non-configurationality. Evaluation of the strength of their pairwise correlation shows that null direct objects and discontinuous NPs are deeply intertwined.