Characterizing network flows is essential for security operators to enhance their awareness about cyber-threats targeting their networks. The automation of network flow characterization with machine learning has received much attention in recent years. To this aim, raw network flows need to be transformed into structured and exploitable data. In this research work, we propose a method to encode raw network flows into robust latent representations exploitable in downstream tasks. First, raw network flows are transformed into graph-structured objects capturing their topological aspects (packet-wise transitional patterns) and features (used protocols, packets' flags, etc.). Then, using self-supervised learning techniques like Graph Auto-Encoders and Anonymous Walk Embeddings, each network flow graph is encoded into a latent representation that encapsulates both the structure of the graph and the features of its nodes, while minimizing information loss. This results in semantically-rich and robust representation vectors which can be manipulated by machine learning algorithms to perform downstream network-related tasks. To evaluate our network flow embedding models, we use probing flows captured with two /20 network telescopes and labeled using reports originating from different sources. The experimental results show that the proposed network flow embedding method allows for reliable darknet probing activity classification. Furthermore, a comparison between our self-supervised approach and a fully-supervised graph convolutional network shows that, in situations with limited labeled data, the downstream classification model that uses the derived latent representations as inputs outperforms the fully-supervised graph convolutional network. There are many applications of this research work in cybersecurity, such as network flow clustering, attack detection and prediction, malware detection, vulnerability exploit analysis, and inference of attacker's intentions.