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Graph classification plays an important role is data mining, and variousmethods have been developed recently for classifying graphs. In this paper, wepropose a novel method for graph classification that is based on homotopyequivalence of graphs. Graphs are called homotopy equivalent if one of them canbe converted to the other one by contractible transformations. A basic graphand the complexity of a homotopy equivalence class are defined andinvestigated. It is shown all graphs belonging to a given homotopy equivalenceclass have similar topological properties and are represented by a basic graphwith the minimal number of points and edges. Diagrams are given of basic graphswith the complexity N<7. The advantage of this classification is that it relieson computer experiments demonstrating a close connection between homotopyequivalent topological spaces and homotopy equivalent graphs.

Classification of graphs based on homotopy equivalence. Homotopy  equivalent graphs. Basic graphs and complexity of homotopy equivalence  classes of graphs