The structural analysis is a processing step during which graphs are extracted from binary images. We can decompose the structural analysis into local and global approaches. The local approach decomposes the connected components, and the global approach groups them together. This paper deals especially with the local structural analysis. The local structural analysis is employed for different applications like symbol recognition, line drawing interpretation, and character recognition. We propose here a primer on the local structural analysis. First, we propose a general decomposition of the local structural analysis into four steps: object graph extraction, mathematical approximation, high-level object construction, and object graph correction. Then, we present some considerations on the method comparison and combination.