Carbonate platform background fracture networks are rarely utilized in subsurface models, and it is unclear how they relate to regional stress (other than faults and folds) and burial. We combine structural analysis and drone imagery to investigate the geometry, kinematics, and topological characteristics of (background) fractures at the Latemar platform (both limestones and dolostones; Northern Italy). Deformation was accommodated by a dense network of mode I and conjugate hybrid fractures/veins and conjugate reverse faults, all associated with sub-vertical stylolites. Conjugate fractures and associated sub-vertical stylolites are organized in two systems, constraining the major stress fields. Differences lie in the permutation of the position in the space of the principal stress with depth. Specific burial depth windows are significant in distinguishing the different spatial positions of the principal stresses. Changes in overburden provide the major driving factor in determining the position of background structures that develop during the burial trajectory. Topologically, background fractures in lime- and dolostone pavements show distinct characteristics. In limestone pavements, fractures form a network with a high proportion of I-node and I-C to C-C branches, resulting in a low to moderate connectivity (i.e., C_B = ~ 1.5). In dolostones, a complex network with abundant Y-to X- nodes and I-C to C-C branches is found (moderate to a high degree of connectivity C_B = ~ 1.7). Topological pathways provide important insights into how background fractures are connected and shed light on the significance of these features in the context of subsurface fluid flow.