text: 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.