We present a novel and efficient pore-network extraction (PNE) platform that utilizes a seamless merging algorithm to extract core-sized pore networks directly from high-resolution segmented micro-computed tomography images of rock samples. This platform has the distinct advantage of being parallel friendly, allowing the entire computational workload of the extraction process to be distributed across multiple compute nodes. The superior computational efficiency of this approach paves the way for the extraction of deterministic pore networks with physical dimensions that are comparable to those of core samples employed in conventional core-flooding experiments. Sensitivity analysis studies are performed on digital replicates of Berea and Bentheimer sandstone rock samples. To illustrate the role of a user-defined adjustment coefficient on the extraction process, a set of conventional-sized pore networks are extracted and analyzed for both rock samples. To ascertain the quality of these pore networks, comparisons are made with equivalent pore networks extracted using a well-characterized open-source pore-network extractor. After rigorous examination of these conventional-sized pore networks, the validated PNE platform is applied to extract miniature-core-sized pore networks, and their relevant statistics and petrophysical properties are presented. In addition, these networks are extensively utilized in both quasi-static and dynamic pore-network modeling (PNM) simulations of two-phase flow processes. The predicted two-phase flow properties of the rock samples are benchmarked against the corresponding experimental data and the results are presented in both the current and the second volume of this work.