Before revision:  A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws  .
After revision:  A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws . These central results are resumed in the relation a + b = s^Y between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s^Y .