In this paper, a graph signal denoising method based on heat kernel smoothing (HKS) and its distributed implementation structures are investigated. First, the graph signal denoising problem and HKS method are briefly described. Because HKS method needs to perform eigen-decomposition of graph Laplacian matrix for computing matrix exponential, it is only suitable for centralized implementation. To obtain a distributed or decentralized implementation of HKS method, three implementation methods are then presented in this study including product expansion method, Taylor series expansion method and numerical differentiation approximation method. Finally, irregular data collected from sensor network and social network are used to demonstrate the effectiveness of the graph signal denoising methods based on heat kernel smoothing.