  A metric graph is a 1-dimensional stratified metric space consisting of
vertices and edges or loops glued together. Metric graphs can be naturally used
to represent and model data that take the form of noisy filamentary structures,
such as street maps, neurons, networks of rivers and galaxies. We consider the
statistical problem of reconstructing the topology of a metric graph embedded
in R^D from a random sample. We derive lower and upper bounds on the minimax
risk for the noiseless case and tubular noise case. The upper bound is based on
the reconstruction algorithm given in Aanjaneya et al. (2012).
