A robust stability criterion is derived for a class of higher order consensus algorithms. In distinction to the standard consensus problem where the dynamics of all individual agents are the same and of low dimension, the criterion for reaching consensus now depends on the full spectrum of the communication graph and not only the largest nonzero eigenvalue. The new consensus criterion is posed as a Nyquist-like criterion that provides a clear separation between the individual dynamics and the spectrum of the graph. Our results are illustrated on a formation control problem for a target encircling task.