Conserved cycles in a biochemical network can be identified by examination of the stoichiometry matrix,  The stoichiometry matrix for a simple cycle with species A and AP is given by:
The rates of change of A and AP can be written using the equation:
Expanding the expression leads to:
Note that . This means that , where  is the total mass of moiety .
Given an arbitrary system:
elementary row operations can be applied to both sides such that the stoichiometric matrix is reduced to its echelon form,  giving:
The elementary operations are captured in the  matrix. We can partition  to match the echelon matrix where the zero rows begin such that:
By multiplying out the lower partition, we obtain:
The  matrix will contain entries corresponding to the conserved cycle participants.