An Introduction to Graph Theory and Its Applications

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GROUP 6 — GRAPHS Data Structures & Algorithms What is a Graph? A graph is a data structure made of vertices and edges. Vertices are also called nodes. Edges connect the vertices together. Graphs are used to represent relationships and networks. Graphs vs Trees Trees are special graphs without cycles. Graphs can contain loops and multiple paths. Trees have a hierarchical structure. Graphs are more flexible for complex systems. Vertices and Edges Vertices are points inside the graph. Edges represent the connection between vertices. Edges may be directed or undirected. Edges can also store weights or costs. Directed Graphs Directed graphs have one-way connections. The direction of the edge is important. Twitter follow system is an example. Used in web links and road maps. Undirected Graphs Undirected graphs have two-way connections. Both vertices are equally connected. Facebook friendship is an example. Useful in communication networks. Weighted Graphs Weighted graphs assign values to edges. Weights may represent distance or time. Used in GPS and airline systems. Helpful in optimization problems. Adjacency List Stores neighbors of every node in lists. Efficient for sparse graphs. Easy to implement in Python. Requires less memory. Adjacency Matrix Uses rows and columns to store edges. 1 means connected and 0 means not connected. Good for dense graphs. Requires more memory than adjacency lists. BFS and DFS BFS explores nodes level by level. DFS explores deeply before backtracking. BFS uses queues. DFS uses recursion or stacks. Real-Life Applications Graphs are used in Google Maps. Social media platforms use graphs. Internet systems form huge graphs. Flight routes are represented using graphs. THANK YOU Any Questions?

This presentation provides a comprehensive introduction to graph theory, covering fundamental concepts such as vertices, edges, and graph types (directed, undirected, weighted). It explores different graph representations, essential traversal algorithms like BFS and DFS, and illustrates their diverse real-world applications in technology and networks.

May 15, 202611 slides

Slide 1 of 11

Slide 1 - GROUP 6 — GRAPHS

GROUP 6 — GRAPHS

An Introduction to Graph Theory and Its Applications

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Photo by Conny Schneider on Unsplash

Slide 2 of 11

Slide 2 - What is a Graph?

A graph is a data structure made of vertices and edges.
Vertices are also called nodes.
Edges connect the vertices together.
Graphs are used to represent relationships and networks.

Slide 3 of 11

Slide 3 - Graphs vs Trees

Graphs Can contain loops and multiple paths. More flexible for complex systems.

Trees Special graphs without cycles. Have a hierarchical structure.

Slide 4 of 11

Slide 4 - Vertices and Edges

Vertices are points inside the graph.
Edges represent the connection between vertices.
Edges may be directed or undirected.
Edges can also store weights or costs.

Slide 5 of 11

Slide 5 - Directed Graphs

Directed graphs have one-way connections.
The direction of the edge is important.
Twitter follow system is an example.
Used in web links and road maps.

Slide 6 of 11

Slide 6 - Undirected Graphs

Undirected graphs have two-way connections.
Both vertices are equally connected.
Facebook friendship is an example.
Useful in communication networks.

Slide 7 of 11

Slide 7 - Weighted Graphs

Weighted graphs assign values to edges.
Weights may represent distance or time.
Used in GPS and airline systems.
Helpful in optimization problems.

Slide 8 of 11

Slide 8 - Graph Representations

Adjacency List Stores neighbors of every node in lists. Efficient for sparse graphs. Easy to implement in Python. Requires less memory.

Adjacency Matrix Uses rows and columns to store edges. 1 means connected and 0 means not connected. Good for dense graphs. Requires more memory than adjacency lists.