arXiv:2610.15393v2 Announce Type: replace Abstract: A model of propagation and accumulation of errors caused by round-off errors during conjugate gradient (CG) iterations is proposed, based on their interpretation as iterations of traversals of the linear system matrix graph. In the matrix graph, vertices correspond to the components of the search direction, residual, and approximate solution vectors, which are computed recursively at CG iterations. It is shown that when the number of CG iterations performed is less than the distance between two vertices in the graph, the round-off errors arising in the computation of one component do not affect the errors in the computation of another and are not correlated. At early iterations, errors propagate locally between neighboring vertices and are locally correlated. As the errors become sufficiently global, loss of orthogonality of residuals and conjugacy of search directions occurs, and stagnation of the iterative process sets in. The results of computational experiments are presented for matrices corresponding to graphs with a prescribed diameter, for Laplacians of differential equations, and for random matrices. These results demonstrate that the diameter and its approximate values, in particular the pseudodiameter, due to their low computational cost for sparse graphs, can be used in mixed-precision algorithms for solving linear systems, namely, for switching precision modes as round-off errors propagate and accumulate.