Graph mining has emerged as a significant field of research with applications spanning multiple domains, including marketing, corruption analysis, business, and politics. The exploration of knowledge within graphs has garnered considerable attention due to the exponential growth of graph-modeled data and its potential in applications where data relationships are a crucial component, and potentially being even more important than the data themselves. However, the increasing use of graphs for data storing and modeling presents unique challenges that have prompted advancements in graph mining algorithms, data modeling and storage, query languages for graph databases, and data visualization techniques. Despite there being various methodologies for data analysis, they predominantly focus on structured data and may not be optimally suited for highly connected data. Accordingly, this work introduces a novel methodology specifically tailored for knowledge discovery in labeled and heterogeneous graphs (KDG), and it presents three case studies demonstrating its successful application in addressing various challenges across different application domains.