  The problem of finding the connected components of a graph is considered. The
algorithms addressed to solve the problem are used to solve such problems on
graphs as problems of finding points of articulation, bridges, maximin bridge,
etc. A natural approach to solving this problem is a breadth-first search, the
implementations of which are presented in software libraries designed to
maximize the use of the capabi\-lities of modern computer architectures. We
present an approach using perturbations of adjacency matrix of a graph. We
check wether the graph is connected or not by comparing the solutions of the
two systems of linear algebraic equations (SLAE): the first SLAE with a
perturbed adjacency matrix of the graph and the second SLAE with~unperturbed
matrix. This approach makes it possible to use effective numerical
implementations of SLAE solution methods to solve connectivity problems on
graphs. Iterations of iterative numerical methods for solving such SLAE can be
considered as carrying out a graph traversal. Generally speaking, the traversal
is not equivalent to the traversal that is carried out with breadth-first
search. An algorithm for finding the connected components of a graph using such
a traversal is presented. For any instance of the problem, this algorithm has
no greater computational complexity than breadth-first search, and for~most
individual problems it has less complexity.
