  In 2002 Freiberg and Z\"ahle introduced and developed a harmonic calculus for
measure-geometric Laplacians associated to continuous distributions. We show
their theory can be extended to encompass distributions with finite support and
give a matrix representation for the resulting operators. In the case of a
uniform discrete distribution we make use of this matrix representation to
explicitly determine the eigenvalues and the eigenfunctions of the associated
Laplacian.
