Table 1 Overview of the real-world networks used in the experiments.

From: The effect of distant connections on node anonymity in complex networks

Network	Nodes	Edges	Fraction twins	\(max-\ell\)	Runtime d-k-anonymity		Runtime Anonymity-cascade		Type
Network	Nodes	Edges	Fraction twins	\(max-\ell\)	d = 1	d = 2	\(C_1\)	\(C_{ max-\ell }\)	Type
Radoslaw emails³²	167	3250	0.072	3	0.02 s	+ < 0.01 s	+ < 0.01 s	+ < 0.01 s	Communication
Primary school³³	236	5899	0.000	1	0.02 s	+ < 0.01 s	+ < 0.01 s	+ < 0.01 s	Human contact
Moreno innov.³²	241	923	0.025	3	< 0.01 s	+ < 0.01 s	+ < 0.01 s	+ < 0.01 s	Communication
Gene fusion³²	291	279	0.753	6	< 0.01 s	+ < 0.01 s	+ < 0.01 s	+ < 0.01 s	Biological
Copnet calls¹³	536	621	0.287	10	< 0.01 s	+ 0.01 s	+ < 0.01 s	+ < 0.01 s	Communication
Copnet sms¹³	568	697	0.285	7	< 0.01 s	+ 0.01 s	+ < 0.01 s	+ < 0.01 s	Communication
Copnet FB¹³	800	6418	0.005	4	0.02 s	+ 0.01 s	+ < 0.01 s	+ < 0.01 s	Online social
FB Reed98³⁴	962	18,812	0.012	3	0.05 s	+ 0.01 s	+ 0.01 s	+ 0.02 s	Online social
Arenas email³²	1133	5451	0.042	5	0.02 s	+ 0.01 s	+ < 0.01 s	+ < 0.01 s	Communication
Network science³²	1461	2742	0.755	6	0.01 s	+ 0.01 s	+ < 0.01 s	+ < 0.01 s	Co-autorship
FB Simmons81³⁴	1518	32,988	0.011	3	0.12 s	+ 0.02 s	+ 0.01 s	+ 0.02 s	Online social
DNC emails³²	1893	4385	0.706	4	0.02 s	+ 0.38 s	+ < 0.01 s	+ < 0.01 s	Online social
Moreno health³²	2539	10,455	0.003	5	0.03 s	+ 0.04 s	+ < 0.01 s	+ < 0.01 s	Human social
FB Wellesley22³⁴	2970	94,899	0.000	4	0.4 s	+ 0.07 s	+ 0.04 s	+ 0.08 s	Online social
Bitcoin alpha³⁴	3783	14,124	0.306	5	0.04 s	+ 0.36 s	+ < 0.01 s	+ 0.01 s	Online social (trust)
GRQC collab.³⁵	5242	14,484	0.455	8	0.03 s	+ 0.04 s	+ < 0.01 s	+ < 0.01 s	Co-autorship
FB Carnegie49³⁴	6637	249,967	0.008	4	1.37 s	+ 0.44 s	+ 0.09 s	+ 0.18 s	Online social
Pajek Erdős³²	6927	11,850	0.737	6	0.02 s	+ 0.19 s	+ 0.01 s	+ 0.02 s	Co-autorship
DT interaction³⁶	7341	15,138	0.572	12	0.07 s	+ 2.88 s	+ < 0.01 s	+ < 0.01 s	Biological
DG assoc.³⁶	7813	21,357	0.531	8	0.21 s	+ 5.13 s	+ < 0.01 s	+ < 0.01 s	Biological
FB GWU54³⁴	12,193	469,528	0.006	4	2.64 s	+ 0.92 s	+ 0.18 s	+ 0.36 s	Online social
Anybeat³⁴	12,645	49,132	0.500	5	0.41 s	+ 1.34 h	+ 0.02 s	+ 0.04 s	Online social
CE-CX³⁴	15,229	245,952	0.021	6	1.04 s	+ 1.56 s	+ 0.09 s	+ 0.19 s	Biological
Astro Physics³⁴	18,771	198,050	0.305	6	0.72 s	+ 1.91 s	+ 0.05 s	+ 0.11 s	Co-autorship
FB BU10³⁴	19,700	637,528	0.006	4	3.17 s	+ 1.44 s	+ 0.25 s	+ 0.50 s	Online social
FB Uillinois³⁴	30,664	1,048,574	0.002	4	5.96 s	+ 2.66 s	+ 0.39 s	+ 0.78 s	Online social
Enron email³⁵	36,692	183,831	0.528	6	0.90 s	+ 1.44 m	+ 0.06 s	+ 0.12 s	Communication
FB Penn94³⁴	41,536	1,362,220	0.002	4	8.95 s	+ 5.39 s	+ 0.50 s	+ 1.00 s	Online social
FB wall 2009³²	46,952	183,412	0.133	8	0.54 s	+ 1.80 s	+ 0.05 s	+ 0.13 s	Communication
Brightkite³⁴	58,228	214,078	0.258	8	0.78 s	+ 18.41 s	+ 0.06 s	+ 0.14 s	Online social
The marker cafe³⁷	69,413	1,644,843	0.200	5	37.96 s	+ 10.46 m	+ 0.67 s	+ 1.35 s	Human contact
Slashdot zoo³²	79,116	467,731	0.274	7	3.36 s	+ 2.62 m	+ 0.15 s	+ 0.34 s	Online social
Twitter³²	465,017	833,540	0.801	5	59.53 s	+ 6.04 h	+ 0.29 s	+ 0.62 s	Online social
DBLP³²	1,824,701	8,344,615	0.402	10	51.37 s	+ 11.58 m	+ 28.1 s	+ 57.18 s	Co-autorship
Flixster³²	2,523,386	7,918,801	0.631	8	3.10 m	+ 8.57 h	+ 18.58 s	+ 37.81 s	Online social
Youtube³²	3,223,585	9,375,374	0.336	15	13.24 m	+ > 1 week	+ 30.68 s	+ 1.04 m	Online social

For each network, we list the number of nodes, edges, fraction of twin nodes, the highest attained cascading level (\(max-\ell\)) and runtimes of the experiments performed containing the total runtime (\(d=1)\) and runtime additional to computing \(d=1\), indicated by “+” for \(d=2\), \(C_1\) and \(C_{ max-\ell }\).

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Table 1 Overview of the real-world networks used in the experiments.

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