  In this article we review known results on parameterized linear codes over
graphs, introduced by Renter\'ia, Simis and Villarreal in 2011. Very little is
known about their basic parameters and invariants. We review in detail the
parameters dimension, regularity and minimum distance. As regards the parameter
dimension, we explore the connection to Eulerian ideals in the ternary case and
we give new combinatorial formulas.
