# 14 Difference Between Tree And Graph |(Tree Vs Graph)

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In programming, data can be stored in data structures like graphs and trees. A tree is typically special form of graph i.e minimally connected graph and having only one path between any two vertices.  In other words tree is a special case of graph having no loops, circuits and no-self loops. Graphs can have loops, circuits as well as can have self-loops.

## Trees

Tree in data structures is a hierarchical data structure which stores information naturally in the form of hierarchy style.  Trees are used to define data structures and as a basis for algorithms to solve problems. When compared to arrays, linked lists, stacks and queues which are linear data structures, a tree is a nonlinear data structure.

Just like a graph, a tree data structure is a collection of nodes. The nodes can then have children nodes. The children nodes can have their own children nodes referred to as grandchildren nodes. For example, the HTML DOM uses a tree data structure to represent the hierarchy of elements.

### Terms Associated With Trees

• Root Node:  This is the topmost node of the tree.
• Child: This is the node that is connected by parent nodes.
• Edge: Edges are used to connect two nodes.
• Parent Node: The root node in the structure having one or more than one reference node or pointing to other nodes.
• Leaf Node: This is the node that does not have any child in the structure.
• Level: A level can be regarded as the height of a tree. In tree, the height ascends from Top to bottom, where root node lay at 0 level and the leaf node lay at the bottom of a tree or subtree.

## What You Need To Know About Trees (Properties)

1. Tree is special form of graph i.e minimally connected graph and having only one path between any two vertices.
2. Trees data structures are hierarchical, non-linear collections of linked nodes.
3. In trees there are many rules/restrictions for making connections between nodes through edges.
4. Different types of trees based different properties include binary tree, binary search tree, AVL tree, Heaps etc.
5. Pre-order, in-order, and post-order are some kind of the logarithms that are used in trees to through all elements.
6. An example of a tree is the HTML DOM where every other tag flows hierarchically from the html doctype tag.
7. A tree cannot have a loop structure.
8. Trees can be categorized as DAG (Directed Acyclic Graphs). DAG is a kind of directed graph that has no cycles.
9. In trees there is parent-child relationship, every child can have only one parent and therefore, the flow can be from top to bottom direction or vice versa.
10. In trees, there is exactly one root node and each child has only one parent.
11. If trees have “n’’ vertices than it must have exactly “n-1’’ edges only.
12. Trees are less complex when compared to graphs because they do not have cycles and self-loops but still connected.
13. Tree is a special case of graph having no loops, no circuits and self-loops.
14. Used in sorting, searching, traversing and binary search.

## Graph

Graphs in JavaScript programming are a data structure comprising of a collection of nodes with edges. An edge is a pair of nodes that are connected. They are primarily used to describe a model that shows the route from one location to another location. A graph can be directed or undirected.

A directed graph contains edges which function similar to a one-way street. The edges flow from one node to another.  For example you can have a graph of people and cars or TVs where each person can have several favorite cars or TVs but cars or TVs do not have a favorite person.

An undirected graph has edges which flow bi-directionally, similar to a two-lane road with traffic going both directions.  For example, you can have a graph of goats whereby each goat has an owner and each owner has a goat.

### Terms Associated With Graph

• Cycle: This is a path where the first and the last vertices are same.
• Path: A path from a random vertex w is an adjacent sequence of vertices.
• Vertices: Vertices are the nodes present on the graph, connected with the help of edges.
• Degree:  It is the number of edges incident on a vertex.
• Connected Graph: in case there is a path from a random vertex to any other vertex, then the graph can be described as connected Graph.

## What You Need To Know About Graph (Properties)

1. In graph there can be more than one path i.e graph can have uni-directional or bi-directional path (edges) between nodes.
2. Graphs data structures are collections of linked nodes in non-linear network models.
3. In graphs no restrictions/rules are there for connecting the nodes through edges.
4. There are only two types of graphs based on different properties, that is, directed and Undirected Graphs.
5. Breath First Search, Depth First Search are some kind of searching algorithms in graphs to traverse through each element.
6. A good example of a network graph is a map of a road within a city.
7. A graph can have a loop structure, which means the last element and the first element are same.
8. Graph can be Cyclic or Acyclic.
9. In graphs there is no parent-child relationship.
10. There is no concept of root node in graphs.
11. In graphs, the number of edges does not depend on the number of vertices.
12. Graphs are more complex when compared to trees because it has cycles and loops.
13. Graph can have loops, circuit as well as self-loops.
14. Some applications of graph include coloring of maps, job scheduling, used in algorithms of data science and machine learning.

## Difference Between Tree And Graph In Tabular Form

 BASIS OF COMPARISON TREE GRAPH Description Tree is special form of graph i.e minimally connected graph and having only one path between any two vertices. In graph there can be more than one path i.e graph can have uni-directional or bi-directional path (edges) between nodes. Structure Trees data structures are hierarchical, non-linear collections of linked nodes. Graphs data structures are collections of linked nodes in non-linear network models. Rules/Restrictions In trees there are many rules/restrictions for making connections between nodes through edges. In graphs no restrictions/rules are there for connecting the nodes through edges. Types Binary tree, binary search tree, AVL tree, Heaps etc. Directed and Undirected Graphs. Search Algorithm Pre-order, in-order, and post-order are some kind of the logarithms that are used in trees to through all elements. Breath First Search, Depth First Search are some kind of searching algorithms in graphs to traverse through each element. Example An example of a tree is the HTML DOM where every other tag flows hierarchically from the html doctype tag. A good example of a network graph is a map of a road within a city. Loop Structure A tree cannot have a loop structure. A graph can have a loop structure, which means the last element and the first element are same. Categories Trees can be categorized as DAG (Directed Acyclic Graphs). DAG is a kind of directed graph that has no cycles. Graph can be Cyclic or Acyclic. Parent-Child Relationship In trees there is parent-child relationship, every child can have only one parent and therefore, the flow can be from top to bottom direction or vice versa. In graphs there is no parent-child relationship. Concept of Root Node In trees, there is exactly one root node and each child has only one parent. There is no concept of root node in graphs. Edges And Vertices If trees have “n’’ vertices than it must have exactly “n-1’’ edges only. In graphs, the number of edges does not depend on the number of vertices. Complexity Trees are less complex when compared to graphs because they do not have cycles and self-loops but still connected. Graphs are more complex when compared to trees because it has cycles and loops. Components Tree is a special case of graph having no loops, no circuits and self-loops. Graph can have loops, circuit as well as self-loops. Application Used in sorting, searching, traversing and binary search. Some applications of graph include coloring of maps, job scheduling, used in algorithms of data science and machine learning.
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