While increasing Arctic temperatures have been identified to induce widespread thermokarst development in permafrost lowland landscapes over only several decades, disturbances, such as tundra fires can cause similar impacts within a few years. Transition from low-centered to high-centered polygons through the formation of troughs is an immediate result of melting ice wedges 3-4 years after a fire (Jones et al., 2015). Liljedahl et al (2016) have shown that widespread ice-wedge degradation can lead to hydrological connectivity and increased drainage of entire landscapes through newly developing trough networks. Quantifying such dynamics is important for projecting the hydrological outcomes of climate change impacts across vast Arctic landscapes. New VHR remote sensing approaches allow assessing ice wedge polygonal structures and their change in unprecedented detail. Data science methods provide valuable tools for understanding and modeling resulting very large datasets of changing ice wedge networks. Here we quantify thermokarst development representing the network of troughs as a graph, a concept from discrete mathematics used to model complex networks. Our analysis is based on optical VHR aerial imagery of the DLR MACS sensors and DSMs derived from LiDAR. Datasets are available for 2009, 2014 and 2019 of the northern Anaktuvuk River Fire scar in Alaska, which formed due to a large tundra fire in 2007. In particular, the post-fire permafrost degradation is observable in the northern ice-rich region of the fire scar on short timescales, offering an ideal site for the monitoring of degradation processes. We use morphological image analysis to extract a graph from the imagery and further deduce trough parameters, such as soil volume, depth, and water availability. Quantifying these factors for the study area shows that soil erosion and ice melt within individual troughs have progressed, while the overall connectivity of the network has increased, implying strong thermo-erosion since 2009. Using graphs to monitor the ongoing development offers a detailed and computationally efficient method that will allow quantification of ice-wedge degradation over very large spatial and temporal scales and may provide useful metrics for projecting landscape trajectories in thaw-vulnerable permafrost environments.