This deliverable defines and exemplifies the structure for representing both the global as well as the personal model of a learning scenario to the MaTHiSiS learners, namely the MaTHiSiS Learning Graphs (LGs). It further describes the library implementation that handles the creation, access and modification of the Learning Graphs, namely the LG lib, as well as the corresponding Open API implementation used to seamlessly access the features of LG lib throughout the MaTHiSiS platform. This is the second and final iteration of this document, rounding the modelling strategy, the RESTful services that are offered through the MaTHiSiS ecosystem and the front-end interface used to create, view, access and modify Learning Graphs, with the additional report of updates since the first iteration of this document and first version of these components.