The risk of node re-identification in labeled social graphs

Applied Network Science

Table 1 Graph properties of the real network datasets

Network	\|N\|		\|E\|			p	τ	\(\hspace {-2pt}\bar {d}\)	C	r	κ
	R(%)	B(%)	R−R(%)	B−B(%)	R−B(%)
polblogs	1224		16718					0.02	0.22	−0.22	2.49
(party)	48	52	44	48	8	0.48	0.84
fb-caltech	769		16656					0.05	0.29	−0.06	1.33
(gender)	91.5	8.5	92.8	0.2	7	0.08	0.52
(occupation)	72	28	69	8	23	0.28	0.42
fb-dartmouth	7694		304076					0.01	0.15	0.04	2.76
(gender)	86.5	13.5	83.2	0.9	15.9	0.14	0.34
(occupation)	62	38	58	18	24	0.38	0.5
fb-michigan	30147		1176516					0.0026	0.13	0.115	3.05
(gender)	92.2	7.8	90.5	0.2	9.3	0.08	0.37
(occupation)	77.5	22.5	72	9	19	0.22	0.46
pokec-1	265388		700352			0.46	0	2×10⁻⁵	0.0068	−0.044	5.66
(gender)	46	54	18.6	22.4	59
amazon-products	303551		835326			0.18	0.99	1.8×10⁻⁵	0.21	−0.06	17.42
(category)	82	18	83.4	16.4	0.2

All graphs are undirected, and nodes are annotated with a binary valued attribute. E.g., nodes in the polblogs network have the attribute party with values; conservative and liberal. For simplicity, binary values are presented using the notation of R and B, together with the distributions of such values over nodes and edges. p and τ present the estimated parameter values of the attraction model. Density \((\bar {d})\) is the fraction of all possible edges, transitivity (C) is the fraction of triangles of all possible triangle in the network. degree-assortativity (r) measures the similarity of relations depending on the associated node degree. Average path length (κ) depicts the average shortest path length between any pairs of nodes