Characteristic of a (directed) tree is the fact that every node is the head of exactly one arc (every node has exactly one arrow pointing to it), with one exception. The root node, or simply root, is distinguished by the fact that it is not the head of any arc (no arrow points to it). It is customary to draw a tree upside down, with the root at the top. See Fig 2.2a.

The leaves of a tree are nodes which are not the tail of any ars (there are no arrows pointing away from them).

The fact that only one arrow points to each node (except for the root) prevents any loops in a tree. At the end of any loop two arrows would point to the same node. The tree cannot be a loop because there must be a root which has no arrow pointing to it.

In most text books on graph theory a tree is drawn as a ugraph. In Fig 2.2b the arcs sloping downward in Fig 2.2a have been replaced by the edges under them (the arrows are replaced by undirected line segments). It is assumed that the root is always at the top, the highest place in the ugraph. This method of drawing a tree is the most convenient.

The fact that each node in the directed tree is a head (except for the root) forces the underlying ugraph to be connected.

Replacing the arcs of a directed tree by edges produces the underlying ugraph, called the underlying or undirected tree. The undirected tree is always connected and without loops. See