Research ArticleSOCIAL NETWORKS

Leaking privacy and shadow profiles in online social networks

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Science Advances  04 Aug 2017:
Vol. 3, no. 8, e1701172
DOI: 10.1126/sciadv.1701172
  • Fig. 1 Shadow profile problem.

    Diagram of the shadow profile problem, where the network contains a fraction t of the final size and users in the network have a tendency r to share their contact lists.

  • Fig. 2 Radar plots of sexual orientation and relationship status in individual neighborhoods.

    Each point in a radar plot has a distance from the center corresponding to the logarithm of the normalized ratios of neighbors of each orientation and relationship status. Each radar plot corresponds to one class of relationship status or sexual orientation. Relationship status displays a pattern of assortativity with the same status, and sexual orientation displays a more complex mixing pattern with homophily for homosexual users and heterophily for gender for heterosexual users. Hof, homosexual female; Hom, homosexual male; Bif, bisexual female; Bim, bisexual male; Hef, heterosexual female; Hem, heterosexual male.

  • Fig. 3 Predictor performance inside the social network.

    ROC curves of the predictors of sexual orientation (left) and relationship status (middle). The shaded areas show the maximum and minimum values of the predictor performance in a 100-fold evaluation. The diagonal dashed line is the result of the same analysis with permuted profiles [area under the curve (AUC) = 0.499]. In both cases, neighborhood information in the social network predicts individual information. Right: AUC for various values of the disclosure tendency to share personal information publicly in the social network. Error bars show SD of 100 samples given the value of the disclosure tendency. AUC increases with disclosure tendency in both cases.

  • Fig. 4 Shadow profile predictor performance.

    Predictor performance (AUC) versus t and ρ for sexual orientation and relationship status. Each value is computed as the mean of 100 samples for each combination of t and ρ values. In both cases, predictor performance increases with network size and tendency to share contact lists.

  • Table 1 Kendall correlation coefficients of predictor performance (AUC) versus t and ρ.

    Estimates are median values of bootstrap distributions and confidence intervals are calculated at the 95% level. P values result from permutation tests with 10,000 permutations of the AUC values. AUCs of both sexual orientation and relationship status increase monotonically with t and ρ. This effect is multiplicative, reaching high τ values for the correlation between AUC and the product of t and ρ. All these observations are robust to the same tests with partial correlation coefficients and significant with P < 0.05 in permutation tests.

    CoefficientSexual orientationRelationship status
    EstimateConfidence intervalPEstimateConfidence intervalP
    τ(AUC, t)0.4760.465–0.488<0.050.5820.573–0.592<0.05
    τ(AUC, ρ)0.5690.558–0.5780.4640.453–0.475<0.05
    τ(AUC, t·ρ)0.9510.949–0.952<0.050.9410.940–0.943<0.05
    τ(AUC, t | ρ)0.5790.573–0.585<0.050.6570.652–0.663<0.05
    τ(AUC, ρ | t)0.6470.641–0.653<0.050.5710.565–0.577<0.05
    τ(AUC, ρ | t)0.9360.935–0.938<0.050.9180.917–0.920<0.05
    τ(AUC, ρ | ρ)0.9300.928–0.932<0.050.9260.924–0.927<0.05

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/8/e1701172/DC1

    Text A: Mixing patterns of sexual orientation at distances 2 and 3

    Text B: Prediction performance details

    fig. S1. Radar plots of sexual orientation at neighborhoods at distances 2 and 3.

    fig. S2. Mixing patterns of sexual orientation at distances 1 to 3.

    fig. S3. Predictor performance versus t and ρ.

    fig. S4. Bootstrapping and permutation tests of the correlation between sexual orientation AUC and t, ρ, and their product.

    fig. S5. Bootstrapping and permutation tests of the correlation between relationship status AUC and t, ρ, and their product.

    fig. S6. Bootstrapping and permutation tests of the partial correlation between sexual orientation AUC and t, ρ, and their product.

    fig. S7. Bootstrapping and permutation tests of the partial correlation between relationship status AUC and t, ρ, and their product.

  • Supplementary Materials

    This PDF file includes:

    • Text A: Mixing patterns of sexual orientation at distances 2 and 3
    • Text B: Prediction performance details
    • fig. S1. Radar plots of sexual orientation at neighborhoods at distances 2 and 3.
    • fig. S2. Mixing patterns of sexual orientation at distances 1 to 3.
    • fig. S3. Predictor performance versus t and ρ.
    • fig. S4. Bootstrapping and permutation tests of the correlation between sexual orientation AUC and t, ρ, and their product.
    • fig. S5. Bootstrapping and permutation tests of the correlation between relationship status AUC and t, ρ, and their product.
    • fig. S6. Bootstrapping and permutation tests of the partial correlation between sexual orientation AUC and t, ρ, and their product.
    • fig. S7. Bootstrapping and permutation tests of the partial correlation between relationship status AUC and t, ρ, and their product.

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