Two nodes may be connected by a series of arcs. A path is a sequence of distinct arcs (no nodes repeated) connecting the nodes. A directed path from node i to node j is a sequence of arcs, each of whose direction (if any) is towards j. An undirected path may have directed arcs pointed in either direction.
A path that begins and ends at the same node is a cycle and may be either directed or undirected.
A network is connected if there exists an undirected path between
any pair of nodes. A connected network without any cycle is called a tree,
mainly because it looks like one.