I consider a repeated trust game played between a group of insiders, arranged in a network representing their lines of communication, and a single outsider. Insiders follow a local punishment rule, shunning the outsider if it has cheated them or a neighbor. The object of interest is that the outsider may know either summary statistics about the nature of the network, or know its precise non-anonymous structure. For the outsider to have knowledge of the precise structure may, depending on the shape of the network, increase or decrease the volume of honest interaction that can be sustained. In extreme cases, a small 'local' vulnerability to outside exploitation can result in a total breakdown of the chance for mutually beneficial trade across the whole network. Strategic ignorance and obfuscation of network structure may therefore be valuable to both sides, complicating the problem for a network operator seeking to monetize data on the network graph. I discuss recent decisions by Twitter and Facebook in this framework.