  The goal of this paper is to provide a general purpose result for the
coupling of exploration processes of random graphs, both undirected and
directed, with their local weak limits when this limit is a marked
Galton-Watson process. This class includes in particular the configuration
model and the family of inhomogeneous random graphs with rank-1 kernel.
Vertices in the graph are allowed to have attributes on a general separable
metric space and can potentially influence the construction of the graph
itself. The coupling holds for any fixed depth of a breadth-first exploration
process.
