Unit Disk Graph Based Modelling of a Network of Mobile Agents

This contribution addresses the problem of communication topology changes induced by the movement of a set of mobile agents. The network is modeled as a unit disk graph (UDG) where each unit disk is centered in a node and where the communication topology is given by the instantaneous agents position. UDG allows for a compact representation of the communication topology as an intersection of unit disks. Fundamental properties of UDG are then used to characterize the feasible communication topologies. Under certain mobility assumptions, we show that all the transitions between the set of induced graphs are possible provided that the cardinality of the corresponding set of edges are different at most by one element.