Detecting overlapping communities based on vital nodes in complex networks<xref rid="cpb_27_10_100504_fn1" ref-type="fn">*</xref><fn id="cpb_27_10_100504_fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 61672124, 61370145, 61173183, and 61503375) and the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund, China (Grant No. MMJJ20170203).</p></fn>

Detecting overlapping communities based on vital nodes in complex networks**

Project supported by the National Natural Science Foundation of China (Grant Nos. 61672124, 61370145, 61173183, and 61503375) and the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund, China (Grant No. MMJJ20170203).

Wang Xingyuan^{1, 2, †}, Wang Yu², Qin Xiaomeng², Li Rui³, Eustace Justine²

(color online) Two communities and four overlapping vertices in friendship network from Zachary’s karate club study.