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f - connection: a new circuit concept

The node-to node connection of the respective nodes of lumped circuits of the same topology is considered. An interesting feature of some relevant resistive (more generally, algebraic) structures shows that this connection is unjustly ignored in the classical theory of resistive circuits. The circuit situation under study is useful in the analysis of the input conductivity of some grid cuts (even infinite grids) composed of nonlinear elements, which is relevant to percolation conductivity (a problem of modern solid-state physics), the lumped-elements modeling of some nonlinear media, spatial filtering, and some other problems.