Difference between graph and tree

Graph :

A graph is a collection of two sets V and E where V is a finite non-empty set of vertices and E is a finite non-empty set of edges.

• Vertices are nothing but the nodes in the graph.
• Two adjacent vertices are joined by edges.
• Any graph is denoted as G = {V, E}.

For Example:

G = {{V₁, V₂, V₃, V₄, V₅, V₆}, {E₁, E₂, E₃, E₄, E₅, E₆, E₇}} Tree :

A tree is a finite set of one or more nodes such that –

1. There is a specially designated node called root.
2. The remaining nodes are partitioned into n>=0 disjoint sets T₁, T₂, T₃, …, T_n
   where T₁, T₂, T₃, …, T_n are called the subtrees of the root.

The concept of a tree is represented by following Fig.

Graph vs Tree

The basis of Comparison	Graph	Tree
Definition	Graph is a non-linear data structure.	Tree is a non-linear data structure.
Structure	It is a collection of vertices/nodes and edges.	It is a collection of nodes and edges.
Edges	Each node can have any number of edges.	If there is n nodes than there would be n-1 number of edges
Types of Edges	They can be directed or undirected	They are always directed
Root node	There is no unique node called root in graph.	There is a unique node called root(parent) node in trees.
Loop Formation	A cycle can be formed.	There will not be any cycle.
Traversal	For graph traversal, we use Breadth-First Search (BFS), and Depth-First Search (DFS).	We traverse a tree using in-order, pre-order, or post-order traversal methods.
Applications	For finding shortest path in networking graph is used.	For game trees, decision trees, the tree is used.

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