  In social networks, different users may have different privacy preferences
and there are many users with public identities. Most work on differentially
private social network data publication neglects this fact. We aim to release
the number of public users that a private user connects to within n hops,
called n-range Connection fingerprints(CFPs), under user-level personalized
privacy preferences. We proposed two schemes, Distance-based exponential budget
absorption (DEBA) and Distance-based uniformly budget absorption using Ladder
function (DUBA-LF), for privacy-preserving publication of the CFPs based on
Personalized differential privacy(PDP), and we conducted a theoretical analysis
of the privacy guarantees provided within the proposed schemes. The
implementation showed that the proposed schemes are superior in publication
errors on real datasets.
