Nowadays, remote sensing technologies produce huge amounts of satellite images that can be helpful to monitor geographical areas over time. A satellite image time series (SITS) usually contains spatio-temporal phenomena that are complex and difficult to understand. Conceiving new data mining tools for SITS analysis is challenging since we need to simultaneously manage the spatial and the temporal dimensions at the same time. In this work, we propose a new clustering framework specifically designed for SITS data. Our method firstly detects spatio-temporal entities, then it characterizes their evolutions by mean of a graph-based representation, and finally it produces clusters of spatio-temporal entities sharing similar temporal behaviors. Unlike previous approaches, which mainly work at pixel-level, our framework exploits a purely object-based representation to perform the clustering task. Object-based analysis involves a segmentation step where segments (objects) are extracted from an image and constitute the element of analysis. We experimentally validate our method on two real world SITS datasets by comparing it with standard techniques employed in remote sensing analysis. We also use a qualitative analysis to highlight the interpretability of the results obtained.