Check non-manifold edges
The non-manifold edges are the edges that belong to three faces or more. In B-rep modeling kernels, it is advantageous to have a non-manifold topology to construct ad-hoc idealized simulation models. Analysis Situs shows non-manifold edges in yellow right after the model is loaded.
In the model above, the non-manifold topology serves to represent the compartments of a ship hull. The nice implication of having extra non-manifold sharing between the B-rep elements is that it brings conformal mesh subdomains when tessellated for FEA. To get non-manifold edges in Analysis Situs, use the corresponding GUI button in the "Analysis" panel.
It is worth mentioning that non-manifoldness is the property of a geometric kernel. Therefore, to design and analyze non-manifold B-rep entities, one does not have to apply any non-trivial algorithms: all information is encoded right in the topology graph.