Social networks are of significant importance in various application domains. Understanding the general properties of real social networks has gained much attention due to the proliferation of networked data. Many applications of networks such as anonymous web browsing and data publishing require relationship anonymity due to the sensitive, stigmatizing, or confidential nature of the relationship. One general approach for this problem is to randomize the edges in true networks, and only release the randomized networks for data analysis. Our research focuses on the development of randomization techniques such that the released networks can preserve data utility while preserving data privacy.Data privacy refers to the sensitive information in the network data. The released network data after a simple randomization could incur various disclosures including identity disclosure, link disclosure and attribute disclosure. Data utility refers to the information, features and patterns contained in the network data. Many important features may not be preserved in the released network data after a simple randomization. In this dissertation, we develop advanced randomization techniques to better preserve data utility of the network data while still preserving data privacy. Specifically we develop two advanced randomization strategies that can preserve the spectral properties of the network or can preserve the real features (e.g., modularity) of the network. We quantify to what extent various randomization techniques can protect data privacy when attackers use different attacks or have different background knowledge. To measure the data utility, we also develop a consistent spectral framework to measure the non-randomness (importance) of the edges, nodes, and the overall graph. Exploiting the spectral space of network topology, we further develop fraud detection techniques for various collaborative attacks in social networks. Extensive theoretical analysis and empirical evaluations are conducted to demonstrate the efficacy of our developed techniques.
