Manual creation of trail maps for hikers is time-consuming and can be inaccurate. This paper presents a new method to construct trail networks based on a growing self-organizing map (GSOM) using publicly available Global Positioning System (GPS) data. Unlike other network topology construction techniques, this approach is not dependent on sequential GPS traces. Fine-tuning multiple hyperparameters enables to customize this process based on unique features of datasets and networks. The generated maps, which are trained on public GPS data, are compared to a ground truth from Open Street Map (OSM). The performance evaluation is based on the accuracy, completeness, and topological correctness of the trail maps. The proposed approach outperforms, particularly on sparse networks without significant GPS noise.