Two prominent genetic programming approaches are the graph-based Cartesian Genetic Programming (CGP) and Linear Genetic Programming (LGP). Recently, a formal algorithm for constructing a directed acyclic graph (DAG) from a classical LGP instruction sequence has been established. Given graphbased LGP and traditional CGP, this paper investigates the similarities and differences between the two implementations, and establishes that the significant difference between them is each algorithm's means of restricting interconnectivity of nodes. The work then goes on to compare the performance of two representations each (with varied connectivity) of LGP and CGP to a directed cyclic graph (DCG) GP with no connectivity restrictions on a medical classification and regression benchmark.