In this paper, we formalize the notion of distributed sensitive social networks (DSSNs), which encompasses networks like enmity networks, financial transaction networks, supply chain networks and sexual relationship networks. Compared to the well studied traditional social networks, DSSNs are often more challenging to study, given the privacy concerns of the individuals on whom the network is knit. In the current work, we envision the use of secure multiparty tools and techniques for performing privacy preserving social network analysis over DSSNs. As a step towards realizing this, we design efficient data-oblivious algorithms for computing the K-shell decomposition and the PageRank centrality measure for a given DSSN. The designed data-oblivious algorithms can be translated into equivalent secure computation protocols. We also list a string of challenges that are needed to be addressed, for employing secure computation protocols as a practical solution for studying DSSNs.