Sparsification of the U.S. mobility network: average fraction of disconnected nodes.

The average fraction of nodes disconnected from the largest connected component of the network by sparsifiers of different types. The horizontal axis shows the fraction of edges of the original network preserved by the sparsifier. Even when only 1% of the edges are preserved, effective resistance keeps almost all the nodes connected, while uniform and weight-based sampling disconnects 5% and 7% of the nodes respectively.