  Even more interesting than the intricate organization of complex networks are
the dynamical behavior of systems which such structures underly. Among the many
types of dynamics, one particularly interesting category involves the evolution
of trails left by moving agents progressing through random walks and dilating
processes in a complex network. The emergence of trails is present in many
dynamical process, such as pedestrian traffic, information flow and metabolic
pathways. Important problems related with trails include the reconstruction of
the trail and the identification of its source, when complete knowledge of the
trail is missing. In addition, the following of trails in multi-agent systems
represent a particularly interesting situation related to pedestrian dynamics
and swarming intelligence. The present work addresses these three issues while
taking into account permanent and transient marks left in the visited nodes.
Different topologies are considered for trail reconstruction and trail source
identification, including four complex networks models and four real networks,
namely the Internet, the US airlines network, an email network and the
scientific collaboration network of complex network researchers. Our results
show that the topology of the network influence in trail reconstruction, source
identification and agent dynamics.
