  A visualized graph is a powerful tool for data analysis and synthesis tasks.
In this case, the task of visualization constitutes not only in displaying
vertices and edges according to the graph representation, but also in ensuring
that the result is visually simple and comprehensible for a human. Thus, the
visualization process involves solving several problems, one of which is the
problem of constructing a topological drawing of a planar part of a non-planar
graph with a minimum number of removed edges. In this manuscript, we consider a
mathematical model for representing the topological drawing of a graph, which
is based on methods of the theory of vertex rotation with the induction of
simple cycles that satisfy the Mac Lane planarity criterion. It is shown that
the topological drawing of a non-planar graph can be constructed on the basis
of a selected planar part of the graph. The topological model of a graph
drawing allows us to reduce the brute-force enumeration problem of identifying
a plane graph to a discrete optimization problem - searching for a subset of
the set of isometric cycles of the graph that satisfy the zero value of the Mac
Lane's functional. To isolate the planar part of the graph, a new computational
method has been developed based on linear algebra and the algebra of structural
numbers. The proposed method has polynomial computational complexity.
