Agroforestry systems are complex due to the diverse interactions between their elements, and they develop over several decades. Existing numerical models focus either on the structure or on the functions of agroforestry systems. However, these both aspects are necessary, as function influences structure and vice versa. Here, we present a representation of agroforestry systems based on combinatorial maps (which are a type of multidimensional graphs), that allows conceptualizing the structure-function relationship at the agroecosystem scale. We show that such a model can represent the structure of agroforestry systems at multiple scales and its evolution through time. We propose an implementation of this framework, coded in Python, which is available on GitHub. In the future, this framework could be coupled with knowledge based or with biophysical simulation models to predict the production of ecosystem services. The code can also be integrated into visualization tools. Combinatorial maps seem promising to provide a unifying and generic description of agroforestry systems, including their structure, functions and dynamics, with the possibility to translate to and from other representations.