  We tackle the problem of simultaneous transformations of networks represented
as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or
parallel rewrite relations over complex structures such as graphs: (i) those
which transform disjoint subgraphs in parallel and hence can be simulated by
successive mere sequential and local transformations and (ii) those which
transform overlapping subgraphs simultaneously. In the latter situations,
parallel transformations cannot be simulated in general by means of successive
local rewrite steps. We investigate this last problem in the framework of
overlapping graph transformation systems. As parallel transformation of a graph
does not produce a graph in general, we propose first some sufficient
conditions that ensure the closure of graphs by parallel rewrite relations.
Then we mainly introduce and discuss two parallel rewrite relations over
graphs. One relation is functional and thus deterministic, the other one is not
functional for which we propose sufficient conditions which ensure its
confluence.
