In this paper, we consider learning problems defined on graph-structured data. We propose an incremental supervised learning algorithm for network-based estimators using diffusion kernels. Diffusion kernel nodes are iteratively added in the training process. For each new node added, the kernel function center and the output connection weight are decided according to an empirical risk driven rule based on an extended chained version of the Nadaraja-Watson estimator. Then the diffusion parameters are determined by a genetic-like optimization technique.