What is the difference between an undirected and a directed Graph?

Undirected and Directed graphs are fundamental concepts in graph theory, it is basically a branch of mathematics that deals with the study of graphs and it consists of a set of vertices(nodes) connected by edges. 

In this article, we will learn the differences between an undirected and a directed graph.,

Undirected Graphs

An undirected graph is a graph where the edges do not have a specific direction and it is bidirectional in nature it does not have a parent-child relation concept as there is no particular direction.

Example of an undirected graph

Characteristics of Undirected Graphs:

• Symmetry:

Symmetry is present in the undirected graph as each edge is bidirectional, so it’s not like anyone’s the boss. The graph is connected, so you can always find a way to get to any node you want to, and the degree of each vertex tells you how popular that node is in the graph.

• Connectivity:

There is just one method to get from one vertex to another in an undirected graph which indicates that the graph is linked.

Algorithms for Undirected Graphs

• Breadth-First Search (BFS) 
• Depth-First Search (DFS) 

Directed Graphs

A directed graph is a graph that is unidirectional in this the edges have a specific direction and the edges have directions specified with them also a directed graph can contain cycles.

Example of a directed graph

Characteristics of Directed Graphs

• Asymmetry:

Asymmetry is present in the directed graph as the edges are all one-way, so it’s not like everyone is on equal footing and the graph might not be connected, which means there might be some nodes that are totally out of the loop.

• Connectivity:

In a directed graph, there may be more than one way to traverse from one vertex to another which means that the graph may not be connected.

Algorithms for Directed Graphs:

• Topological Sort
• Dijkstra’s Algorithm

Differences between Undirected Graph & Directed Graph:

S.N	Undirected Graph	Directed Graph
1	It is simple to understand and manipulate.	It provides a clear representation of relationships with direction.
2	It has the symmetry of a relationship.	It offers efficient traversal in the specified direction.
3	It requires less memory hence memory efficient.	It is suitable for modeling processes or workflows.
4	It provides limited modeling capability for directed relationships	It is complex as compared to undirected graphs.
5	Inefficient traversal without additional checks.	It has a lack of symmetry, unlike an undirected graph.
6	It is difficult to represent specific scenarios.	It may require increased memory usage compared to undirected graphs.

Applications of Undirected Graph:

• Social Networks: In social networks, you can use undirected graphs to model them. You see, each vertex in the graph represents an individual, and each edge represents a friendship or a connection between those individuals.
• Traffic flow optimization: Undirected graphs are also used to model road networks and each vertex will represent an intersection or an endpoint, and each edge represents a road.

Applications of Directed Graph:

• Computer networks: Directed graphs are basically a way to represent the internet as a bunch of devices connected. 
• Project management: Directed graph in project management the vertices will represent different tasks and the edges represent the dependencies between them. So basically, it’s a way to make sure everything gets done in the right order.