Component
A component (also "connected component") of an undirected graph is a collection of nodes that are connected by neighbor links: every node in a connected component is reachable from every other node in the component. See https://en.wikipedia.org/wiki/Component_(graph_theory). Such a graph is said to be "fully connected" iff it has a single component, or it is empty.
Parameters
start
the lowest-numbered node in the component
size
the number of nodes in the component