We revisit the proposal that colour confinement is related to the dynamics of magnetic monopoles using methods derived from Topological Data Analysis, which provide a mathematically rigorous characterisation of topological properties of quantities defined on a lattice. After introducing homology, we discuss how this concept can be used to quantitatively analyse the behaviour of Abelian monopoles identified through the Maximal Abelian Projection across the deconfinement phase transition of SU(3) Yang-Mills. Specifically, we define an observable called “simplicity”, which measures the number of
connected components over the number of topologically non-trivial loops in a current network. A finite-size scaling analysis of the ensemble-averaged simplicity of Abelian magnetic monopole currents provides the expected value of the
critical coupling with an accuracy that is generally higher than that obtained with conventional thermodynamic approaches at comparable statistics. Initial results for QCD are also discussed.