The quest to identify genetic factors that shape the human brain has been greatly accelerated by imaging. The human brain functions as a complex network of integrated systems and connected processes, and a vast number of features can be observed and extracted from structural brain images -- including regional volume, shape, and other morphological features of given brain structures. This feature set can be considered as part of the structural network of the brain, which is under strong genetic control. However, it is unclear which of the imaging derived features serve as the most promising traits for discovering specific genes that affect brain structure. Here, we aim to create the first ever network of genetically correlated cortical sulcal features, and through a twin model, determine the degree of genetic correlation across the entire network. Building on functional brain network analysis, we consider the high-dimensional genetic correlation structure as a undirected graph with a complex network of multi-weighted hubs to uncover the underlying genetic core of sulcal morphometry.