  In recent years, discrete spaces such as graphs attract much attention as
models for physical spacetime or as models for testing the spirit of
non-commutative geometry. In this work, we construct the differential algebras
for graphs by extending the work of Dimakis et al and discuss linear
connections and curvatures on graphs. Especially, we calculate connections and
curvatures explicitly for the general nonzero torsion case. There is a metric,
but no metric-compatible connection in general except the complete symmetric
graph with two vertices.
