Tree vs Forest in Graph theory

In graph theory, a tree and a forest are both special types of graphs that do not contain cycles.

Here is difference between tree and forest.

	Tree	Forest
Definition	A connected acyclic graph	A collection of disjoint trees
Components	Only one tree	Multiple trees
Connectivity	All vertices are connected	Each tree is connected but trees are disjoint
Cycles	No cycles	No cycles in individual trees
Number of Edges	n-1 (where n is the number of vertices)	Sum of edges in all trees
Root	A tree can have a designated root vertex	Each tree in the forest can have its root
Paths	Unique path between any two vertices	Paths are unique within each tree
Examples	Family tree, hierarchical structure	Multiple disconnected network components
Examples