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HomeHomework HelpmathematicsGraph Theory

Graph Theory

The study of graphs, which are non-linear data structures consisting of nodes or vertices connected by edges, with applications in computer science, mathematics, and other fields, including graph traversal, shortest paths, and network analysis

intermediate
5 hours
Mathematics
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Overview

Graph theory is a vital area of mathematics that explores the relationships between objects through graphs. It provides tools to model and analyze various systems, from social networks to transportation routes. Understanding the basic components of graphs, such as vertices and edges, is essential fo...

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Key Terms

Vertex
A point in a graph where edges meet.

Example: In a social network graph, each person is a vertex.

Edge
A connection between two vertices in a graph.

Example: In a road map, each road is an edge connecting two locations.

Path
A sequence of edges that connects a sequence of vertices.

Example: A path from A to B through C is A-C-B.

Cycle
A path that starts and ends at the same vertex without repeating edges.

Example: A-B-C-A forms a cycle.

Directed Graph
A graph where edges have a direction, indicated by arrows.

Example: A Twitter follower relationship is a directed graph.

Undirected Graph
A graph where edges have no direction.

Example: A friendship relationship is an undirected graph.

Related Topics

Network Theory
Study of complex networks and their properties.
intermediate
Combinatorics
Mathematics of counting and arrangement.
intermediate
Algorithms
Study of step-by-step procedures for calculations.
advanced

Key Concepts

VerticesEdgesPathsCycles