Table 1.

Main properties of the data sets used in the present study. N: number of nodes, L: number of edges, $⟨k⟩$: average degree, $k_{max}$: maximum degree, $⟨ks⟩$: average value of the $k$-shell index, D: maximum value of the $k$-shell index, $N_{\text{c}}^{\mathtt{Lvn}}$, $Q^{\mathtt{Lvn}}$: number of communities determined by the Louvain method and the corresponding modularity, respectively, $N_{\text{c}}^{\mathtt{SBM}}$, $Q^{\mathtt{SBM}}$: number of communities determined by the SBM and the corresponding modularity, respectively.

Data set	N	L	$⟨k⟩$	$k_{max}$	$⟨k_{\text{s}}⟩$	D	$N_{\text{c}}^{\mathtt{Lvn}}$	$Q^{\mathtt{Lvn}}$	$N_{\text{c}}^{\mathtt{SBM}}$	$Q^{\mathtt{SBM}}$	References
Facebook 1	4039	88234	43.691	1045	26.880	115	16	0.835	62	0.551	55,74
Facebook 2	6386	217662	68.168	930	35.712	56	19	0.419	198	0.158	56–58,75
Facebook 3	2235	90954	81.391	467	44.508	63	8	0.436	87	0.139	56–58,76
Facebook 4	11247	351358	62.480	415	32.413	63	10	0.438	274	0.193	56–58,77
Facebook 5	27737	1034802	74.615	2555	38.681	81	18	0.470	547	0.172	56–58,78
Twitter	81306	1342296	33.018	3383	17.762	96	73	0.808	510	0.511	55,79
Web-blogs	1490	16715	22.436	351	12.154	36	275	0.426	17	0.076	60,80
Emails	1005	16064	31.968	345	17.063	34	26	0.410	33	0.232	81–83
Cond. Matter	23133	93439	8.078	279	4.900	25	619	0.730	203	0.633	83,84
Comp. Science	317080	1049866	6.622	343	4.215	113	209	0.822	676	0.726	59,85,86
Global airline	3376	19179	11.362	248	6.123	31	26	0.665	40	0.311	61
Words	146005	656999	9.000	1008	5.289	31	378	0.759	548	0.583	59,87,88
Cookpad Greece	32235	745178	46.234	8196	23.709	158	40	0.166	76	0.020	–
Cookpad Spain	122158	1749751	28.647	12637	14.547	162	262	0.270	90	0.035	–
Cookpad UK	13758	47525	6.909	1880	3.558	33	199	0.350	8	0.114	–