Representation of denumerable Markov chains with multiple states by weighted circuits

The constructive solution to the problem of representing a strictly stationary Markov chain Sω with a countable infinity of r-sequences (i1,i2,...,ir),r>1, as states by a class of directed weighted circuits is given. Associating the chain Sω with its dual chain η having reversed states and the same transition law, a connection with physical laws that govern diffusion of electrical current through a directed planar network with r-series-connected nodes is shown.