Graphs are expressive abstractions representing more effectively relationships in data and enabling data science tasks. They are also a widely adopted paradigm in causal inference focusing on causal directed acyclic graphs. Causal DAGs (Directed Acyclic Graphs) are manually curated by domain experts, but they are never validated, stored and integrated as data artifacts in a graph data management system. In this paper, we delineate our vision to align these two paradigms, namely causal analysis and property graphs, the latter being the cornerstone of modern graph databases. To articulate this vision, a paradigm shift is required leading to rethinking property graph data models with hypernodes and structural equations, graph query semantics and query constructs, and the definition of graph views to account for causality operators. Moreover, several research problems and challenges arise aiming at automatically extracting causal models from the underlying graph observational data, aligning and integrating disparate causal graph models into unified ones along with their maintenance upon the changes in the underlying data. The above vision will allow to make graph databases aware of causal knowledge and pave the way to data-driven personalized decision-making in several scientific fields.