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) The execution time of our method on artificial networks. (a) N is the number of nodes, γ is the minus exponent for the degree sequence, β is the minus exponent for the community size distribution, μ is the mixing parameter, and ⟨k⟩ is the average degree of network. (b) The used networks are LFR benchmark graphs^[23] with mixing parameter of 0.1, average degree of 15, maximum degree of 50, minimum degree of 20, exponent for the degree distribution of 2, and exponent for the community size distribution of 1.