What is the Difference Between Graph and Tree?

By Mona Kumari|Updated : June 13th, 2022

Difference Between Graph and Tree: In this article, the difference between graph and tree is explained, we will be discussing various parameters based on which these two data structures differ. Graphs and trees are non-linear data structures used to store, traverse and retrieve data. Though the two data structures perform exactly the same task still the difference between the graph and tree exists.

Apart from discussing the major difference between graph and tree, we will also learn about the two data structures individually how are they used to store data, how to find an element stored in them, what is the basic difference and which among the two is preferred most. Let's understand each one individually in the sections given below.

What is the Difference Between Graph and Tree?

Trees and graphs are useful in programming because they depict nonlinear data. A tree is an exception to the rule of graphs in that it does not loop, but graphs can. Both the graph and the tree have certain similarities, but they also have some distinctions. It is an essential topic in the GATE CSE syllabus. Let's look at the difference between a tree and a graph listed in the table below.

Key Difference Between Graph and Tree

 Graph Tree The graph is a non-linear data structure. The tree is a non-linear data structure. It is a collection of vertices/nodes and edges. It is a collection of nodes and edges. A node in a graph can have any number of edges. A tree consists of the nodes having any number of child nodes while a binary tree has at most two child nodes. There is no unique node called the starting node in a graph. There is a unique node called root in trees. A cycle can be present in a graph No cycle can be present in a tree. Applications: For finding the shortest path in the networking, the graph is used. Applications: For game trees, and decision trees, the tree data structure is preferred.

What is a Graph?

The graph is a non-linear data structure. It is a collection of nodes and edges where V represents the finite set and non-empty set of nodes and E represents the finite and non-empty set of edges. The key points to represent a graph are:

• Nodes are nothing but the vertices of the graph.
• Two adjacent nodes are connected by an edge E
• Any graph is denoted by G={V,E}

For example:

What is a Tree?

A tree is a non-linear data structure. It is also referred to as an acyclic graph i.e a graph with no cycles present in it, this is one of the basic differences between a graph and a tree. A tree is a finite set of one or more nodes such that:

• A tree has a special node called the root node.
• The rest of the nodes are partitioned into disjoint sets T1, T2,… Tn where T1, T2,…. Tn is called the subtrees of the root.

For example:

Applications of Graphs and Trees

Graphs and trees are used in various searching and minimizing techniques over the web. The graph data structure is used in minimizing cost from one end to another end, finding the shortest distance between two points/ nodes. The tree data structure is used in the binary search tree, hierarchal trees, organizing trees, and trees are also used in gaming and related fields.

Further, let us see some other related articles.

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FAQs on Difference Between Graph and Tree

• The very basic difference between graph and tree is that a graph consists of cycles while a tree is an acyclic graph that do not consists of any cycle. A tree has zero cycles

• The number of edges difference between graph and tree is as follows. A graph can have a maximum of n(n-1)/2 edges while a tree always consists of n-1 edges. This difference in the number of edges is because of the acyclic graph property of the tree.

• Graph data structure has applications in many fields in computer science, graphs algorithms are widely used by google maps, facebook, image processing etc to find the shortest path or minimized cost.

• To find the shortest distance between two nodes in a graph we have several algorithms such as Dijkstra’s algorithm, Bellmen ford algorithm, Floyd warshall algorithm etc.

• There is a major difference between the number of nodes in a graph and a tree such that a graph can have any number of nodes and no special node present in tree while in tree there is a special node called the root node which is the starting vertex of the tree, every other tree node is referred to as right node and left node.