A fast graph modification method for social network anonymization

•The challenge of algorithm runtime has been addressed.•The graph modification step of the algorithm is focused.•The proposed algorithm has two steps of adding and deleting edges.•It uses an efficient algorithm to select the most appropriate edges.•It improves the algorithm runtime and the utility of the graph. Privacy on social networks is one of the most important and well-known issues. Various algorithms have been proposed to preserve the privacy of social network, all of which try to change the graph structure such that the utility of the graph is maintained. Although these algorithms have been successful in protecting the privacy and the utility of social networks, they are not suitable for anonymizing big data, because of the high cost of processing. Some of these algorithms have a high runtime. In addition, they should be improved from the aspect of preserving graph utility. In this paper, an effective algorithm has been introduced to increase the anonymization speed, as well as improving the graph utility. This algorithm uses number factorization to remove the best edges from the graph in the graph modification step of the algorithm. Since the appropriate edges are selected just through one scan of the edges, the runtime is reduced. In order to add edges to the graph, all the appropriate edges are selected simultaneously and added to the graph using NaFa algorithm. Some limitations are applied to the selection of edges to choose the correct ones. Taking into account the appropriate criteria to select edges in both the removal and addition steps improves the graph utility. The evaluation results of the proposed algorithm on real data sets show the efficiency of the algorithm to sharply reduce the runtime and increase the graph utility, simultaneously.