This graph is a sub-graph of a larger one.
But this sub-graph contains all nodes with a special characteristic.
You can start at any point of the graph. You can reach every other node from there AND get back to where you startet.
Is there a word for such a graph or for the nodes in that graph?
Best Answer
There's no special word for nodes with this property, because if any node $x$ has this property, then all nodes do. Every node $y$ can reach $x$, so $y$ can reach any node in the graph (by first going through $x$) and return to $y$ (because $x$ can reach $y$).
A graph in which all nodes have this property is called strongly connected.
A maximal subgraph in which all nodes can reach each other is called a strongly connected component of the original graph. Within that subgraph, all nodes will have this property: from any node in the subgraph, you can reach every other node in the subgraph and come back.