  Expanders are sparse graph that are strongly connected, where {\it
connectivity} is quantified using eigenvalues of the adjacency matrix, and {\it
sparsity} in terms of vertex valency. We give a model of random graphs and
study their connectivity and sparsity. This model is a particular case of soft
geometric random graphs, and allows to construct sparse graphs with good
expansion properties, as well as highly clustered ones. On those graphs, we
study the speed at which random walks spread in the graph, and visit all
vertices. As an illustration, we build a model for mainland France and study
the spread of random walks under several types of lockdown. Our experiments
show that completely closing medium and long distance travel to slow down the
spread of a random walk is more efficient than than local restrictions.
