  The emergence of social and technological networks has enabled rapid sharing
of data and information. This has resulted in significant privacy concerns
where private information can be either leaked or inferred from public data.
The problem is significantly harder for social networks where we may reveal
more information to our friends than to strangers. Nonetheless, our private
information can still leak to strangers as our friends are their friends and so
on. In order to address this important challenge, in this paper, we present a
privacy-preserving mechanism that enables private data to be diffused over a
network. In particular, whenever a user wants to access another users' data,
the proposed mechanism returns a differentially private response that ensures
that the amount of private data leaked depends on the distance between the two
users in the network. While allowing global statistics to be inferred by users
acting as analysts, our mechanism guarantees that no individual user, or a
group of users, can harm the privacy guarantees of any other user. We
illustrate our mechanism with two examples: one on synthetic data where the
users share their GPS coordinates; and one on a Facebook ego-network where a
user shares her infection status.
