The paper considers the problem of finding critical vertices of an engineering network — such nodes, the removal of which causes maximum damage to the network structure, measured in terms of the number of connected pairs of vertices. Traditionally, it is solved by reducing the problem to an equivalent linear programming problem, but in this case its high dimension leads to significant computational complexity. To reduce the dimension, a preliminary classification of some vertices into critical and non-critical ones is proposed by analyzing their graph characteristics. This allows you to introduce additional constraints to the linear programming problem, which reduces its dimension and speeds up the search for a solution. As a result, the optimal characteristics for classification are determined.: ”closeness coefficient” for critical vertices and ”betweenness centrality” for non-critical vertices.