The literature previously addressed this question of connectivity for random graphs , and we will provide the reader with a brief explanation to motivate our subsequent findings. We will use the phrase 'minimally connected' to refer to a design where a path exists between any pair of nodes. A connected component in a graph is a node or set of nodes that are linked to each other by a path. So, the number of connected components, 𝑐, for a minimally connected design is 1 and for a design without edges, 𝑐 is equal to 𝑛. We provide an illustration of 𝑐 in Fig. . To examine how connectivity changes with 𝑘 for fixed 𝑛, we will consider the Erdős-Rényi model for random graph generation , where edges are independently and randomly selected. The probability of randomly generating a design, 𝒢 𝑖 (𝑛, 𝑘), for fixed 𝑛 and 𝑘 and with edge probability, 𝑝, is the geometric distribution: