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Shape analysis and classification are popular methods for biologists,biophysicists and mathematicians investigating relationships between objectfunction and form. Classic shape descriptors, such as sphericity, can be verypowerful; however, when evaluating complex shapes, these descriptors can beinsufficient for rigorous assessment. Here, we present "ToSkA: TopologicalSkeleton Analysis" a method to analyse complex objects by representing theirshape asymmetries as networks. Using global neighbourhood principles, classicnetwork science metrics and spatial feature embedding we are able to createunique object profiles for classification. It is also possible to track objectsover time and extract significantly different shape features betweenexperiments. Importantly, we have incorporated the capacity to measure absolutespatial features of objects (e.g., branch lengths). This adds additional layersof sensitivity to object classification. Furthermore, because topology is aninherent property of system identity, ToSkA is able to identify segmentationerrors that alter object topology by observing the emergence or loss of cyclesin network representations. Combined, the analytics of ToSkA presented hereallow for the flexibility and in-depth shape profiling necessary for complexobjects often observed in biological and physical settings where robust, yetprecise, system configuration is essential to downstream processes.

ToSkA: Topological Skeleton Analysis for Network-Based Shape Representation and Evaluation of Objects from Cells to Death Stars