  Many applications such as election forecasting, environmental monitoring,
health policy, and graph based machine learning require taking expectation of
functions defined on the vertices of a graph. We describe a construction of a
sampling scheme analogous to the so called Leja points in complex potential
theory that can be proved to give low discrepancy estimates for the
approximation of the expected value by the impirical expected value based on
these points. In contrast to classical potential theory where the kernel is
fixed and the equilibrium distribution depends upon the kernel, we fix a
probability distribution and construct a kernel (which represents the graph
structure) for which the equilibrium distribution is the given probability
distribution. Our estimates do not depend upon the size of the graph.
