  In the regime of two-sample comparison, tests based on a graph constructed on
observations by utilizing similarity information among them is gaining
attention due to their flexibility and good performances for
high-dimensional/non-Euclidean data. However, when there are repeated
observations, these graph-based tests could be problematic as they are
versatile to the choice of the similarity graph. We propose extended
graph-based test statistics to resolve this problem. The analytic p-value
approximations to these extended graph-based tests are derived to facilitate
the application of these tests to large datasets. The new tests are illustrated
in the analysis of a phone-call network dataset. All tests are implemented in
an R package gTests.
