Social and biological networks have led to a huge interest in data analysis on graphs. Various groups within the KDD community have begun to study the task of data mining on graphs, including researchers from database-oriented graph mining, and researchers from kernel machine learning. Their approaches are often complementary, and we feel that exciting research problems and techniques can be discovered by exploring the link between these different approaches to graph mining. This tutorial presents a comprehensive overview of the techniques developed in graph mining and graph kernels and examines the connection between them. The goal of this tutorial is i) to introduce newcomers to the field of graph mining, ii) to introduce people with database background to graph mining using kernel machines, iii) to introduce people with machine learning background to database-oriented graph mining, and iv) to present exciting research problems at the interface of both fields.