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.

翻译：可视化图是数据分析和综合任务的有力工具。在这种情况下，可视化任务不仅包括根据图表示显示顶点和边，还需确保结果对人类而言视觉简洁且易于理解。因此，可视化过程涉及解决若干问题，其中之一便是构建非平面图平面部分的拓扑绘制，同时最小化移除边的数量。本文稿提出了一种表示图拓扑绘制的数学模型，该模型基于顶点旋转理论的方法，通过诱导满足Mac Lane可平面性准则的简单环来实现。研究表明，非平面图的拓扑绘制可以基于图的选定平面部分来构建。图的拓扑绘制模型使我们能够将识别平面图的暴力枚举问题简化为一个离散优化问题——搜索图等距环集合的子集，该子集需满足Mac Lane泛函的零值条件。为分离图的平面部分，我们基于线性代数和结构数代数开发了一种新的计算方法。所提方法具有多项式计算复杂度。