Compute the betweenness centrality of all four vertices ### Graph Theory: Understanding Simple Graphs#### DescriptionThe image depicts a simple undirected graph with 4 vertices and 4 edges. This graph is critical for understanding basic concepts in graph theory, including connectivity and paths.#### Graph Structure- **Vertices**: The graph consists of four vertices labeled 1, 2, 3, and 4.- **Edges**: There are four edges connecting these vertices. - Vertex 1 is connected to Vertex 2. - Vertex 2 is connected to Vertex 3. - Vertex 3 is connected to Vertex 4. - Vertex 2 is also connected to Vertex 4.#### Graph RepresentationThe structure forms a triangle shape with a tail, where:- Vertex 2 serves as a central node connected to the other three vertices (1, 3, and 4). - The triangle base includes vertices 2, 3, and 4, while vertex 1 extends upward, forming a tail connected directly to vertex 2.This type of structure is often a starting point in exploring more complex graph families and network connections, demonstrating fundamental elements like adjacency and paths in graph theory.

Betweenness centrality measures the extent to which a vertex lies on paths between other vertices.…

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Math

Advanced Math

Compute the betweenness centrality of all four vertices

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Compute the betweenness centrality of all four vertices

### Graph Theory: Understanding Simple Graphs

#### Description
The image depicts a simple undirected graph with 4 vertices and 4 edges. This graph is critical for understanding basic concepts in graph theory, including connectivity and paths.

#### Graph Structure
- **Vertices**: The graph consists of four vertices labeled 1, 2, 3, and 4.
- **Edges**: There are four edges connecting these vertices.
- Vertex 1 is connected to Vertex 2.
- Vertex 2 is connected to Vertex 3.
- Vertex 3 is connected to Vertex 4.
- Vertex 2 is also connected to Vertex 4.

#### Graph Representation
The structure forms a triangle shape with a tail, where:
- Vertex 2 serves as a central node connected to the other three vertices (1, 3, and 4).
- The triangle base includes vertices 2, 3, and 4, while vertex 1 extends upward, forming a tail connected directly to vertex 2.

This type of structure is often a starting point in exploring more complex graph families and network connections, demonstrating fundamental elements like adjacency and paths in graph theory.

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