Nonabelian flows in networks

In this work we consider a generalization of graph flows. A flow is, in its simplest formulation, labelling the directed edges with real numbers subject to various constraints. common constraint is conservation vertex, meaning that sum labels on incoming vertex equals those outgoing edges. One easy fact if conserving all but one then it also remaining one. our do not label numbers, elements from an arbitrary group, where becomes false general. As will show, graphs property implies vertices are precisely planar graphs.