Pore-network models are widely used to describe pore-scale flow in porous media, and their reliability depends critically on accurate extraction of pore and throat structures. A new extraction framework, termed the topological pore-network finder, is proposed in this work, which combines topological data analysis, medial access path search, and flashlight search medial axis. The topological data analysis is used to identify pore connectivity and cluster the void space, thereby providing robust initial pore centers. The medial access path search method then traces strings between connected pore centers along the medial axis, while the flashlight search medial axis method is used to refine the resulting paths and improve computational efficiency. The method is validated using toy porous media, two- and three-dimensional digital rock samples. Sensitivity analyses show that the pore-network finder is stable with respect to image resolution and string discretization. Compared with the classical maximal-ball method, the pore-network finder achieves at least an order-of-magnitude acceleration while preserving the main geometric statistics and flow-response characteristics of the extracted networks. In addition, because the method operates in continuous space and can reuse information from previous states, it is well suited to quasi-dynamic updates during deformation. The pore-network finder therefore provides an efficient and accurate tool for pore-network extraction and subsequent pore-scale characterization in geo-energy systems.