Abstract
In the framework of the algebraic approach to looking into characteristics of undirected graphs, the sequence of their matrix representations has been established. The specifics of the matrices in such a sequence makes it possible at last to make a supposition about the explicit form of the Moore-Penrose pseudo inverse of the incidence matrix of an undirected graph. The rightness of the hypothesis has been confirmed by checking using the conditions of Penrose. The usual minimal cuts and shortest paths are shown as objects which are generated by norms introduced into the vector spaces of the edge and vertex flows. If using the Euclidean norm one gets an advantage in doing analysis and synthesis of graphs in comparison to traditional metrics. The proposed metric can be used to generate the behaviour of intelligent agents.
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