Asymptotic connectivity of infinite graphs

We introduce the notion of the asymptotic connectivity of a graph by generalizing to infinite graphs average connectivity as defined by Beineke, Oellermann, and Pippert. Combinatorial and geometric properties of asymptotic connectivity are then explored. In particular, we compute the asymptotic connectivity of a number of planar graphs in order to determine the extent to which this measure correlates with the large-scale geometry of the graph.