  In the first part of this paper, we propose new optimization-based methods
for the computation of preferred (dense, sparse, reversible, detailed and
complex balanced) linearly conjugate reaction network structures with mass
action dynamics. The developed methods are extensions of previously published
results on dynamically equivalent reaction networks and are based on
mixed-integer linear programming. As related theoretical contributions we show
that (i) dense linearly conjugate networks define a unique super-structure for
any positive diagonal state transformation if the set of chemical complexes is
given, and (ii) the existence of linearly conjugate detailed balanced and
complex balanced networks do not depend on the selection of equilibrium points.
In the second part of the paper it is shown that determining dynamically
equivalent realizations to a network that is structurally fixed but
parametrically not can also be written and solved as a mixed-integer linear
programming problem. Several examples illustrate the presented computation
methods.
