Performing some operations on graphs using adjacency matrices

Graph theory is widely used from a practical point of view. Graphs surround us in everyday life (for example, maps of roads and paths), and also play an important role in scientific research (for example, electrical circuits). For everyday use, the geometric way of presenting graphs is certainly the most convenient. But for computer processing of information, this is not rational. In these cases, the matrix representation of graphs is used. Therefore, studies devoted to this topic are gaining more and more importance. This article considers the possibility of performing operations on adjacency matrices that represent graphs. These methods have their own characteristics and limitations. They are also discussed in this article.