Phase unwrapping (PU) is a significant problem for reconstructing the deformation field during Synthetic Aperture Radar Interferometry (InSAR) analysis. The various twodimensional (2-D) PU algorithms can be divided into two categories: (1) path-following methods and (2) optimization based methods. The former predefine an integration path in which the phase gradient is integrated to obtain the unwrapped results. The latter are path-independent and error criterion oriented. The integration of finite differences and the Minimum Cost Flow (MCF) solver describes a global optimization problem between phase residues over closed spatial triangles computed over redundant neighboring edge sets. We propose a modified network using a simplified mathematical formulation for linear programming (LP) in finite differences PU. Our algorithm has three major advantages over current methods. (1) The modified network combines Delaunay triangulation and K nearest points to avoid isolated regions in the PU process. (2) Modified formulation of the LP solver can directly obtain the phase ambiguity cycles of all points without integration. (3) The combination of the new network and modified LP can achieve better PU results than other state-of-the-art techniques. We applied our method to synthetic and real data from the 24, Jan 2020 Mw 6.7 earthquake in Doğanyol-Sivrice, Turkey and the 8, Aug 2017 Mw 6.5 earthquake in Jiuzhaigou, China. Comprehensive comparisons validate the effectiveness of our method. Index Terms-finite differences, linear programming, minimum cost flow (MCF), phase unwrapping, SAR interferometry (InSAR).