Analyzing Private Network Data Using Output Perturbation

Many phenomena can be modeled as networks in which entities (represented by nodes) participate in binary relationships (represented by edges). In a social network, nodes are individuals and edges are personal contacts or relationships. In a communication network, nodes are individuals and edges are flows of information such as phone calls or email messages. In a technological network, nodes are machines, such as computers or power stations, and edges are some means of transmission. Research into the structure and function of networks has wide-ranging applications. Network analysis is being used by businesses to market products [31], by epidemiologists to combat the spread of diseases [32], and by financial regulatory agencies to detect fraud among securities dealers [20]. Network analysis has also been applied to national security, industrial engineering, and computer network design.The collection, dissemination, and analysis of networks has become much easier in recent years. In the early days of social network analysis, data was often collected manually through interviews or surveys. As a result of the cost of data collection, few networks were available to researchers, and those available were small—sometimes consisting of fewer than 100 nodes. Figure 18.1 reproduces a widely studied 34-node social network of karate club members, taken from Zachary [66]. Now, because so many of our interactions leave electronic traces, networks can be systematically recorded, sometimes on a nearly global scale. For example, Leskovec and Horvitz’s [39] study of Microsoft Messenger users examined a network of 180 million nodes and …