  Random walks by single-node agents have been systematically conducted on
various types of complex networks in order to investigate how their topologies
can affect the dynamics of the agents. However, by fitting any network node,
these agents do not engage in topological interactions with the network. In the
present work, we describe random walks on complex networks performed by agents
that are actually small graphs. These agents can only occupy admissible
portions of the network onto which they fit topologically, hence their name
being taken as topologically-specific agents. These agents are also allowed to
move to adjacent subgraphs in the network, which have each node adjacent to the
original respective node of the agent. Two types of random walks are considered
here: uniformly random and influenced by an external field. The performance of
the random walks performed by three types of topologically-specific agents is
studied respectively to the obtained coverage considering three types of
complex networks (geometrical, Erd\H{o}s-R\'enyi, and Barab\'asi-Albert). The
number of nodes displaced at each random walk step is also obtained and
analyzed. Several interesting results are reported and discussed, including the
fact that, despite its intrinsic node degree heterogeneity, Barab\'asi-Albert
networks tend to allow relatively smooth and effective coverage by all the
considered topologically-specific agents. Erd\H{o}s-R\'enyi networks were also
found to yield large dispersions of node coverage. In addition, the triangle
agent was found to allow more effective random walks respectively to any of the
three considered networks.
