  On a compact metric graph, we consider the spectrum of the Laplacian defined
with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower
bound on the gap $\lambda_2 - \lambda_1$ is established, with a constant that
depends only on the total length of the graph and minimum edge length. We also
prove some improvements of known upper bounds for eigenvalue gaps and ratios
for metric trees and extensions to certain other types of graphs.
