Randomizing Social Networks: a Spectrum Preserving Approach

Understanding the general properties of real social networks has gained much attention due to the proliferation of networked data. The nodes in the network are the individuals and the links among them denote their relationships. Many applications of networks such as anonymous Web browsing require relationship anonymity due to the sensitive, stigmatizing, or confidential nature of the re- lationship. One general approach for this problem is to randomize the edges in true networks, and only disclose the randomized net- works. In this paper, we investigate how various properties of net- works may be affected due to randomization. Specifically, we focus on the spectrum since the eigenvalues of a network are intimately connected to many important topological features. We also con- duct theoretical analysis on the extent to which edge anonymity can be achieved. A spectrum preserving graph randomization method, which can better preserve network properties while protecting edge anonymity, is then presented and empirically evaluated.