Connectivity graphs as models of local interactions

In this paper, we study graphs that arise from certain sensory and communication limitations on the local interactions in multi-agent systems. In particular, we show that the set of graphs that can represent formations corresponds to a proper subset of all graphs and we denote such graphs as connectivity graphs. Such graphs have a special structure that allows them to be composed from a small number of atomic crossing generators using a certain kind of graph amalgamation. This structure allows us to give connectivity graphs a useful topological characterization in terms of their simplicial complexes.