Determining whether or not a directed or undirected graph is a tree

Question

I would like to know of a fast algorithm to determine if a directed or undirected graph is a tree.

This post seems to deal with it, but it is not very clear; accordi

Answer 1

An undirected graph is a tree when the following two conditions are true:

1. The graph is a connected graph.
2. The graph does not have a cycle.

A directed graph is a tree when the following three conditions are true:

1. The graph is a connected graph.
2. The graph does not have a cycle.
3. Each node except root should have exactly one parent.