Multivariable dynamical processes are characterized by complex cause and effect relationships among variables. Reconstruction of these causal connections from data, especially based on the concept of Granger causality (GC), has attracted significant attention in process engineering with applications to interaction assessment, topology reconstruction, and fault detection. The standard practice for reconstruction of GC networks has been along the parametric route that deploys vector autoregressive (VAR) models but without giving due importance to the structural characteristics of data generating process (DGP). In this work, we first demonstrate that the presence of a mismatch between model structure and DGP leads to biased and/or inefficient estimates of causality measures and, hence, the strengths (weights) of causal connections. This issue is further aggravated for small sample sizes wherein additionally spurious causal relationships are detected. In this respect, we present, second, a systematic methodology for efficient reconstruction of weighted GC networks for stationary multivariable linear dynamical processes. This methodology uses a combination of sparse optimization and recently introduced scalar correlation functions to select the most appropriate and parsimonious model structure. Applications to synthetic and environmental processes are presented to demonstrate the efficacy of the proposed approach.