Write Main Difference Between Tree and Graph in Data Structures

Graph:

The graph has two sets, which are considered V and E. These vertices are also called nodes, and edges are referred to as arcs connecting any two nodes in a graph. In a simple sentence, we can say that graph- is a set of vertices (V) and edges (E) which is denoted as G (V, E). These are usually accustomed to solving several real-time problems efficiently. These generally represent networks like a city's telephones, circuitry, and paths. These are also used on many social platforms like Facebook, LinkedIn, etc.

Let us consider an example of each user or person on Facebook as a vertex (or node) in the graph. Each vertex has information about the user, like name, gender, etc., and the connection between each node or vertex is considered as edges or arcs. These are also used in the operating system as resource location graphs.

These are also used in Google maps to find the shortest distance between two places, these are also used in airlines to know the best effective route, used in transportation, in circuits it is used to represent the nodes or circuitry points, these are used to solve challenging puzzles like mazes, these are also used in computer networking, there are many advantages of using graphs like it is straightforward to work with the algorithms like DFS and BFS, it has many practical applications, because of its nature(non-linear data structure) it is used in solving many complex problems, it helps in understanding and visualizing complex issues. As we know, every coin has the other side.

Similarly, graphs also have a few disadvantages; they generally use many pointers, which are very difficult to manage and require large memory.

The above figure {1, 2,3,4,5,6} are considered nodes or vertices; these vertices or nodes are connected with the help of edges.

V- Vertices are the essential components in the graph; these vertices are also referred to as vertex or nodes. It is not necessary to label the vertex; it is accepted even if it is not marked.

E- It is a line drawn between any two nodes of the graph to connect. If there is any possible way to connect the nodes, there are no specific rules to combine any two nodes or vertices. Edges are also referred to as arcs. It is not necessary to label every arc or edge; it is accepted even if it is not labelled.

The graph 'G' is denoted as   G = {V, E}.

G = {{V1, V2, V3, V4, V5, V6, V7, V8, V9}, {E1, E2, E3, E4, E5, E6, E7, E8, E9}}

Properties of graphs

1. A node or vertex in a graph can be connected to any other node or vertex in the same graph with the help of edges.
2. An edge can be both undirected as well as bidirected. This means that the edge can relate to a node or vertex in a unidirectional as well as bidirectional manner.
3. An edge can either be weighted or non-weighted.
4. A Graph may contain loops.
5. Nodes or vertices in a given graph may or may not be connected.
6. A graph may or may not contain edges.

Tree:

It is a set that consists of one or more nodes. It is a hierarchical data structure, a non-linear data structure with nodes and edges if you want to store the data or information, which is in the form of a hierarchy.

The above figure represents the structure of the tree

It has roots, internal nodes, external nodes (parent, child), and siblings.

Properties of trees

1. The tree is hierarchical. This means that there is a fixed node on the top of a tree called the root node, and every other node descends this root node.
2. A tree cannot contain any loops.
3. The subsets of the root node in a tree can be further divided into disjoint subsets named subtrees.
4. All the nodes in a tree must be connected.
5. Only a single path exists between any two nodes in a given tree.
6. A tree with n number of nodes contains n – 1 edge.

Differences between trees and graphs

The main differences between trees and graphs are:

1. While trees and graphs fall into non-linear paths, trees provide a better way to represent the relationships between nodes in a hierarchical structure, while graphs are network structures.
2. The tree and figure must relate to the tree's structure, and shapes are not circles if there is no border.
3. Non-linear data consists of a set of objects distributed in a plane; the elements do not have the same order as linear data.
4. A tree has only one path between two edges, while a column has one-way and two-way paths between nodes.
5. A tree has a root, and every child has a parent.
6. A tree has no cycles and autocycles, but a graph has processes and autocycles.
7. Graphs are more complicated because they contain cycles and self-loops. Instead, growing a tree is straightforward.
8. The tree is traversed using sequence, order, and entry strategies.
9. A tree has n-1 vertices. In contrast, the number of edges in a graph is independent and depends on the chart.
10. The tree has a hierarchical structure and a light network structure.
11. Various problems in the computer world are solved using both trees and graphs. This is because a graph contains many connects all the data, which are considered nodes with the help of edges. Trees can be considered as a graph with minimum connections and no loops.