  Repairing inconsistent knowledge bases is a task that has been assessed, with
great advances over several decades, from within the knowledge representation
and reasoning and the database theory communities. As information becomes more
complex and interconnected, new types of repositories, representation languages
and semantics are developed in order to be able to query and reason about it.
Graph databases provide an effective way to represent relationships among data,
and allow processing and querying these connections efficiently. In this work,
we focus on the problem of computing preferred (subset and superset) repairs
for graph databases with data values, using a notion of consistency based on a
set of Reg-GXPath expressions as integrity constraints. Specifically, we study
the problem of computing preferred repairs based on two different preference
criteria, one based on weights and the other based on multisets, showing that
in most cases it is possible to retain the same computational complexity as in
the case where no preference criterion is available for exploitation.
