This work proposes a new methodology for extracting meta-features from graphs representing the behaviour of metaheuristic algorithms for meta-learning applications. In contrast to traditional approaches that rely on problem-specific or program-specific tailored meta-features, the goal is to represent the dynamic behaviour of stochastic algorithms, such as metaheuristics, during their execution, generating a more robust and informative representation for meta-learning applications. The primary motivation is to fill a gap in the literature regarding the construction of generalizable and descriptive meta-representations, which can enrich the knowledge base for automatic selection and configuration of optimisation algorithms. As a case study, five metaheuristic variants were applied to the Travelling Salesman Problem (TSP), with parametrised variations in their components. For each run, behaviour graphs were generated based on their search behaviours. These graphs extracted structural and topological meta-features like connectivity, centrality, and entropy measures. Visualization and analysis tools were used to investigate the expressiveness and quality of these representations. The results indicate that the graph-based approach is promising for separating algorithms in the meta-feature space, enabling the construction of more representative meta-bases and supporting advancements in algorithm recommendation for unseen problems based on behaviour similarity.