Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

Applied Network Science

Table 1 Structural statistics of the real-world social networks: nodes (N), links (L), size of the LCC, size of the LCC as % with respect the total number of network nodes, average node degree \(\left\langle k \right\rangle\), diameter (D), transitivity (C), the edge density and the modularity (Q)

Network	N	L	LCC	LCC (%)	\(\left\langle k \right\rangle\)	D	C	Density	Q
TV Shows	3892	17,262	3892	100	4.4	20.0	0.443	0.00228	0.830
Politician	5908	41,729	5908	100	7.1	14.0	0.429	0.00239	0.815
Government	7057	89,455	7057	100	12.7	10.0	0.433	0.00358	0.614
Public Figures	11,565	67,114	11,565	100	5.8	15.0	0.215	0.00100	0.645
Athletes	13,866	86,858	13,866	100	6.3	11.0	0.303	0.00090	0.637
Company	14,113	52,310	14,113	100	3.7	15.0	0.287	0.00053	0.656
New sites	27,917	206,259	27,917	100	16.2	15.0	0.138	0.00052	0.529
Artist	50,515	819,306	50,515	100	7.4	11.0	0.295	0.00064	0.457
SP500_1	315	8706	315	100	27.6	6.0	0.511	0.08802	0.253
SP500_2	371	10,636	369	99	28.7	6.0	0.718	0.07748	0.373
NetScience	1589	2742	379	24	1.7	17.0	0.878	0.00109	0.954
Email	1005	16,064	986	98	16.0	7.0	0.450	0.01592	0.341

To compute modularity Q, a clustering step was executed in priori using the popular fast-greedy modularity optimization algorithm (Clauset et al. 2004)