  Communities commonly overlap in real-world networks. This is a motivation to
develop overlapping community detection methods, because methods for
non-overlapping communities may not perform well. However, deterioration
mechanism of the detection methods used for non-overlapping communities have
rarely been investigated theoretically. Here, we analyze an accuracy of
spectral clustering, which does not consider overlapping structures, by using
the replica method from statistical physics. Our analysis on an overlapping
stochastic block model reveals how the structural information is lost from the
leading eigenvector because of the overlapping structure.
