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Phosphorylation of specific substrates by protein kinases is a key control mechanism for vital cell-fate decisions and other cellular processes. However, discovering specific kinase-substrate relationships is time-consuming and often rather serendipitous. Computational predictions alleviate these challenges, but the current approaches suffer from limitations like restricted kinome coverage and inaccuracy. They also typically utilise only local features without reflecting broader interaction context. To address these limitations, we have developed an alternative predictive model. It uses statistical relational learning on top of phosphorylation networks interpreted as knowledge graphs, a simple yet robust model for representing networked knowledge. Compared to a representative selection of six existing systems, our model has the highest kinome coverage and produces biologically valid high-confidence predictions not possible with the other tools. Specifically, we have experimentally validated predictions of previously unknown phosphorylations by the LATS1, AKT1, PKA and MST2 kinases in human. Thus, our tool is useful for focusing phosphoproteomic experiments, and facilitates the discovery of new phosphorylation reactions. Our model can be accessed publicly via an easy-to-use web interface (LinkPhinder)., Author summary LinkPhinder is a new approach to prediction of protein signalling networks based on kinase-substrate relationships that outperforms existing approaches. Phosphorylation networks govern virtually all fundamental biochemical processes in cells, and thus have moved into the centre of interest in biology, medicine and drug development. Fundamentally different from current approaches, LinkPhinder is inherently network-based and makes use of the most recent AI developments. We represent existing phosphorylation data as knowledge graphs, a format for large-scale and robust knowledge representation. Training a link prediction model on such a structure leads to novel, biologically valid phosphorylation network predictions that cannot be made with competing tools. Thus our new conceptual approach can lead to establishing a new niche of AI applications in computational biology.