Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (or nodes) and edges. The vertices are the objects of the study, and the edges describe relationships between these objects.
Basic Concepts
- Vertices: These are the individual objects or entities in the graph.
- Edges: These represent the relationships between the vertices.
- Degree: The number of edges connected to a vertex.
- Path: A sequence of vertices connected by edges.
- Cycle: A path that starts and ends at the same vertex.
Types of Graphs
- Undirected Graph: Edges have no direction.
- Directed Graph: Edges have a direction.
- Weighted Graph: Edges have a numerical value associated with them.
Applications
Graph theory has numerous applications in various fields, including:
- Computer Science: Network design, algorithms, and data structures.
- Operations Research: Scheduling, logistics, and network optimization.
- Social Science: Network analysis, social networks, and communication patterns.
For more information on graph theory, you can explore this resource.
Example
Consider a simple social network where people are represented as vertices and friendships as edges. The graph can help analyze the structure of the network, identify influential individuals, and predict the spread of information.
In this graph, each circle represents a person, and the lines represent friendships between them.