  The breakthrough of achieving fully homomorphic encryption sparked enormous
studies on where and how to apply homomorphic encryption schemes so that
operations can be performed on encrypted data without the secret key while
still obtaining the correct outputs. Due to the computational cost, inflated
ciphertext size and limited arithmetic operations that are allowed in most
encryption schemes, feasible applications of homomorphic encryption are few.
While theorists are working on the mathematical and cryptographical foundations
of homomorphic encryption in order to overcome the current limitations,
practitioners are also re-designing queries and algorithms to adapt the
functionalities of the current encryption schemes. As an initial study on
working with homomorphically encrypted graphs, this paper provides an
easy-to-implement interactive algorithm to check whether or not a
homomorphically encrypted graph is chordal. This algorithm is simply a
refactoring of a current method to run on the encrypted adjacency matrices.
