  Clar number and Fries number are two thoroughly investigated parameters of
plane graphs emerging from mathematical chemistry to measure stability of
organic molecules. We consider first a common generalization of these two
concepts for bipartite plane graphs, and then extend it to a framework on
general (not necessarily planar) directed graphs. The corresponding
optimization problem can be transformed into a maximum weight feasible tension
problem which is the linear programming dual of a minimum cost network flow (or
circulation) problem. Therefore the approach gives rise to a min-max theorem
and to a strongly polynomial algorithm that relies exclusively on standard
network flow subroutines. In particular, we give the first network flow based
algorithm for an optimal Fries structure and its variants.
