Table 3 Comparisons with classical community detection algorithms on real networks with ground-truth community labels

	Karate	Football⁵⁹	Polbooks	Polblogs	Cora	Citeseers	Pubmed	Time Complexity
Spin glass⁸⁹	0.61	0.92	0.62	0.88	0.33	0.22	0.21	NA
GN⁸	0.59	0.84	0.80	0.74	0.32	0.23	0.18	O(N³)
GDG⁴⁸	0.91	0.60	0.75	0.66	0.29	0.63	0.19	O(dtN²)
Walktrap⁹⁰	0.51	0.88	0.79	0.88	0.29	0.14	0.16	O\(({N}^{2}\log N)\)
Spectral²³	0.62	0.54	0.70	0.89	0.32	0.25	0.46	O\(({N}^{2}\log N)\)
Inferential^52,56	0.65	0.87	0.77	0.32	0.31	0.40	0.07	O\(({N}^{2}\log N)\)
Fastgreedy²⁵	0.75	0.56	0.78	0.89	0.39	0.28	0.32	O\((N\log N)\)
Infomap²⁶	0.76	0.96	0.69	0.80	0.07	0.04	0.01	O\((N\log N)\)
LPA³⁰	0.88	0.79	0.69	0.91	0.22	0.11	0.18	~ O(E)
Louvain⁹	0.63	0.87	0.70	0.85	0.32	0.27	0.20	~ O(E)
LS	0.83	0.35	0.80	0.69	0.33	0.45	0.46	O(E)

The algorithm with the highest F₁ score is highlighted in bold, and the second highest one is highlighted by underline. Overall, our LS algorithm have a pretty good performance, it is ranked first in two out of seven networks and ranked second in another two when compared to other popular algorithms, some of which are slower but more accurate ones. And our algorithm is the fastest one. For the GDG algorithm, d is the dimension of embedding space, and t is the number of iterations.

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