Recently, a lot of attention has been given to the single graph subsector of Loop Quantum Gravity. Many results therein were obtained with graph-preserving regularisations of the constraints and coherent state techniques. In this talk we will review the most recent achievements and answer questions such as: How can investigations on single graphs help for the complete Loop Quantum Gravity? Can one trust the dynamical predictions obtained via symmetric reduction from cosmological states supported on a lattice? And, what are the quantum corrections sitting on top of the regularised dynamics?