  We introduce and analyze a model of a multi-directed Eulerian network, that
is a directed and weighted network where a path exists that passes through all
the edges of the network once and only once. Networks of this type can be used
to describe information networks such as human language or DNA chains. We are
able to calculate the strength and degree distribution in this network and find
that they both exhibit a power law with an exponent between 2 and 3. We then
analyze the behavior of the accelerated version of the model and find that the
strength distribution has a double slope power law behavior. Finally we
introduce a non-Eulerian version of the model and find that the statistical
topological properties remain unchanged. Our analytical results are compared
with numerical simulations.
