1.
Introduction
2.
What is a Graph?
3.
What is Tree?
4.
Difference Between Graph and Tree
5.
5.1.
What is the difference between tree search and graph search?
5.2.
What makes a graph a tree?
5.3.
What are the methods to traverse a graph?
5.4.
Difference between DFS and BFS?
6.
Conclusion
Last Updated: May 10, 2024
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# Difference Between Graph And Tree

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Ashwin Goyal
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18 Jun, 2024 @ 01:30 PM

## Introduction

What do you understand by graphs and trees? You might have listened to these terms other than in coding, but they play an essential role in the technical rounds of FAANG companies. So these two topics are a must-do for the interviews.

The main similarity between graphs and trees is that they both represent relationships between nodes. However, a key difference is that trees are a special type of graph with a hierarchical structure and no cycles, while graphs can have cycles and arbitrary connections.

## What is a Graph?

graph is a non-linear data structure used to represent the networks, and it consists of vertices(V), or it can be called nodes and edges(E) that connect the pair of nodes.

• In the graph, the edge can be directed or bidirected.
• It can be weighted.

There are two commonly used representations of a graph are:

Graphs are abstract mathematical structures composed of nodes (also called vertices) and edges (also called links or arcs) that connect these nodes. They are widely used to model various real-world systems and relationships, including social networks, transportation networks, computer networks, and more.

One of the key features of graphs is their versatility in representing diverse types of relationships. They can be directed or undirected, depending on whether the edges have a specific direction associated with them. Additionally, graphs can be weighted, meaning that each edge is assigned a numerical value to represent some attribute like distance, cost, or capacity.

Graphs also come in different forms, including sparse graphs with relatively few edges and dense graphs with many edges. Algorithms for traversing, searching, and analyzing graphs play a crucial role in computer science, with applications ranging from pathfinding in maps to recommendation systems in e-commerce.

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## What is Tree?

The tree is a non-linear data structure that offers relationships between the nodes in a structure and consists of nodes and edges, which arranges data items in sorted order and cannot be in the form of a cycle and should always be connected, unlike graphs.

There are several types of trees, such as a binary tree, binary search tree, AVL tree, threaded binary tree, B-tree, etc.

• The topmost node is the tree's root, and all other nodes connected to it are its children(sub-nodes).
• It does not contain any loop.

Trees are hierarchical data structures composed of nodes connected by edges that represent parent-child relationships. Unlike general graphs, trees have a single root node from which all other nodes descend, forming a branching structure without cycles.

One of the key characteristics of trees is their organization into levels, where each level corresponds to nodes at the same distance from the root. This hierarchical arrangement facilitates efficient data storage and retrieval, making trees useful in various applications such as organizing file systems, representing hierarchical data in databases, and implementing search algorithms like binary search trees.

Trees can take different forms, such as binary trees, where each node has at most two children, or balanced trees like AVL trees and red-black trees, which maintain balance to ensure efficient operations. Recursive algorithms are commonly used to traverse and manipulate tree structures, offering efficient solutions for tasks like sorting, searching, and indexing data.

Read Also “Application of Graph data structure

## Difference Between Graph and Tree

Get detailed information about FAANG companies here.

### What is the difference between tree search and graph search?

Tree search involves exploring hierarchical structures with a single root, employing algorithms like depth-first or breadth-first search. Graph search, on the other hand, navigates arbitrary connections, accounting for cycles and diverse node relationships, with algorithms such as Dijkstra's or A*.

### What makes a graph a tree?

A graph becomes a tree when it forms a hierarchical structure without cycles, featuring a single root node from which all other nodes descend. Trees exhibit parent-child relationships, organized into levels, facilitating efficient storage and traversal operations in various applications.

### What are the methods to traverse a graph?

There are two methods to traverse a graph: Depth First Search(DFS) and Breadth-First Search(BFS).

### Difference between DFS and BFS?

DFS uses Stack data structure, and BFS uses Queue data structure.

The Time complexity of BFS is O(V + E) when Adjacency List is used and O(V^2) when Adjacency Matrix is used.

The Time complexity of DFS is also O(V + E) when Adjacency List is used and O(V^2) when Adjacency Matrix is used.

## Conclusion

In this blog, we have covered the two non-linear data structures and how they differ in their properties.

Graphs and trees are used to solve various complex problems in competitive programming. The graph is a Data Structure where vertices are connected using edges and form a cycle. Whereas Trees is a data structure where the topmost node is the tree's root, and all others are its children, it cannot have a cycle.