Fragility of spectral clustering for networks with an overlapping structure

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.Comment: 23 pages, 16 figure