Shape analysis and classification are popular methods for biologists, biophysicists, and mathematicians investigating relationships between function and form. Classic shape descriptors, such as sphericity, can be powerful but may be insufficient for more complex shapes. Here, we present “napari-toska” a topological skeleton-based method to analyze complex shapes by representing their asymmetries as networks. Using global neighborhood principles, classic network science metrics, and spatial feature embedding, we create instance segmentation object profiles for immediate or downstream classification. napari-toska also follows temporal dynamics and identifies network features that differentiate experimental phenotypes. We incorporated absolute spatial feature measurements of objects to retain aspects of scale. Furthermore, napari-toska identifies certain segmentation errors through the emergence or loss of network cycles. Combined, napari-toska functions allow for flexible and in-depth shape profiling of intricate shapes often observed in biological and physical settings where robust, yet precise, system configuration is essential to functionality.