  In this paper, we investigate the stability properties of inverter-based
microgrids by establishing the possible presence of the so-called critical
clusters - groups of inverters with their control settings being close to the
stability boundary. For this, we consider the spectrum of the weighted
admittance matrix of the network and show that its distinct eigenvalues
correspond to inverter clusters, whose structure can be revealed by the
corresponding eigenvector. We show that the maximum eigenvalue of the weighted
admittance matrix corresponds to the cluster, closest to stability boundary. We
also establish, that there exists a boundary on the value of this eigenvalue,
that corresponds to the stability of the overall system. Thus, we make it
possible to certify the stability of the system and find the groups of
inverters in which control settings are closest to the stability boundary.
