In the context of model inversion, a structural invariant of the transfer matrix, the essential order, is used as a model specification criterion to determine the highest time-differentiation order reached by an output in the inverse model. Originally defined for linear time-invariant (LTI) regular systems, we propose an algebraic extension to the class of LTI descriptor systems with regular matrix pencil and show that, from a descriptor system inversion viewpoint, this invariant characterizes the highest time-differentiation of the output like in the regular case. A bond graph determination procedure on the direct model is given using (bi)causal path inspection and the notion of families of different causal paths.