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) Test of our algorithm on the LFR benchmark. The number of nodes is N = 1000, γ is the exponent for the degree distribution, β is the exponent for the community size distribution, and ⟨k⟩ is the average degree. Although not shown in the figure, the average number of overlapping nodes is 10 in all networks. We use two standards NMI (top) and ARI (bottom) simultaneously to measure the detected performance.