An increasing number of methods for control and analysis of power systems relies on representing power networks as weighted undirected graphs. Unfortunately, the presence of outliers in power system graphs may have a negative impact on many of these methods. In addition, detecting outliers can be a relevant task on its own. Motivated by the low number of outlier detection algorithms focusing on weighted undirected graphs, this paper proposes an efficient and effective method to detect loosely connected graph clusters below a certain number of nodes. The essence of the method lies in the efficient examination of the spectral minimal spanning tree of the input graph. The obtained results on several large test power networks validate the high outlier detection performance of the proposed method and its high computational efficiency.