We present the discrete version of heat kernel smoothing on graph data structure. The method is used to smooth data in an irregularly shaped domains in 3D images. New statistical properties of heat kernel smoothing are derived. As an application, we show how to filter out noisy data in the lung blood vessel trees obtained from computed tomography. The method can be further used in representing the complex vessel trees parametrically as a linear combination of basis functions and extracting the skeleton representation of the trees.