  We present an algorithm to grow a graph with scale-free structure of {\it
in-} and {\it out-links} and variable wiring diagram in the class of the
world-wide Web. We then explore the graph by intentional random walks using
local next-near-neighbor search algorithm to navigate through the graph. The
topological properties such as betweenness are determined by an ensemble of
independent walkers and efficiency of the search is compared on three different
graph topologies. In addition we simulate interacting random walks which are
created by given rate and navigated in parallel, representing transport with
queueing of information packets on the graph.
