Edge Local Differential Privacy for Dynamic Graphs

Huge amounts of data are generated and shared in social networks and other network topologies. This raises privacy concerns when such data is not protected from leaking sensitive or personal information. Network topologies are commonly modeled through static graphs. Nevertheless, dynamic graphs better capture the temporal evolution and properties of such networks. Several differentially private mechanisms have been proposed for static graph data mining, but at the moment there are no such algorithms for dynamic data protection and mining. So, we propose two locally ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-differentially private methods for dynamic graph protection based on edge addition and deletion through the application of the noise-graph mechanism. We apply these methods to real-life datasets and show promising results preserving graph statistics for applications in community detection in time-varying networks. The main contributions of this work are: extending the definition of local differential privacy for edges to the dynamic graph domain, and showing that the community structure of the protected graphs is well preserved for suitable privacy parameters.