On analyzing and evaluating privacy measures for social networks under active attack

Abstract

Widespread usage of complex interconnected social networks such as Facebook, Twitter and LinkedIn in modern internet era has also unfortunately opened the door for privacy violation of users of such networks by malicious entities. In this article we investigate, both theoretically and empirically, privacy violation measures of large networks under active attacks that was recently introduced in (Information Sciences, 328, 403-417, 2016). Our theoretical result indicates that the network manager responsible for prevention of privacy violation must be very careful in designing the network if its topology does not contain a cycle. Our empirical results shed light on privacy violation properties of eight real social networks as well as a large number of synthetic networks generated by both the classical Erdös-Rényi model and the scale-free random networks generated by the Barábasi-Albert preferential-attachment model.

A Review of Several Privacy Violation Measures for Large Networks under Active Attacks

“…In [18], DasGupta et al investigated the resistance of 8 real-world network against active attacks with respect to the k, ℓ ðÞ -anonymity. All the networks under investigation were unweighted graphs and the direction of edges (if the network was directed) was ignored during the analysis.…”

“…Results for both ADIM and ADIM ≥ k were obtained by running Algorithm 1 on the networks, the return statements from Algorithm 1 being an exact solution to Problem 2. On the other hand, the exact solution for Problem 1 can be achieved by combining Algorithm 1 and binary search on k to find the largest value of k such that V ≥ k opt 6 ¼ Ø [18].…”

“…[27] 1788 12476 Friendships between users of the website Table 1. List of 8 social networks studied in [18].…”

K-metric antidimension of some generalized Petersen graphs

“…• Privacy violation properties of eight real social networks and large number of synthetic networks generated by both the classical Erdös-Rényi model and the Barbábasi-Albert preferential-attachment model were analyzed in [4];…”

“…For example, wheel graphs studied in [1] are n-metric antidimensional, but for 4 ≤ l ≤ n − 1 there are no l-antiresolving sets in wheel graphs. Therefore, as mentioned and presented in [2,4], it is an interesting problem to find families of graphs for which there exist l-antiresolving sets for all values of l, such that 2 ≤ l ≤ k − 1. In the next two sections we show that GP(n, 1) and GP(n, 2) satisfy the previous property.…”