### Task Instructions1. **Compute Degree Centrality of All Vertices** Calculate the degree centrality for each vertex in the network.2. **Compute Betweenness Centrality of All Vertices** Determine the betweenness centrality for each vertex.3. **Compute Freeman's Centralization Value for Degree and Betweenness** Calculate Freeman's centralization measure for degree centrality and betweenness centrality.4. **Define a Centrality Such That All Four Vertices at the Corner Have Higher Values** Create or identify a centrality measure where the four corner vertices have higher rankings compared to others in the network.### Diagram Description- The diagram depicts a simple undirected graph in the shape of a rectangular grid with two rows and three columns.- There are six vertices total, arranged in two horizontal rows with three vertices each.- Each vertex is connected to its adjacent vertices horizontally and vertically but not diagonally. - The vertices form two parallel lines, with connections forming a total of eight edges.

Degree centrality of a vertex is defined as number of edges linked to that vertex or number of links…

(a) Compute degree centrality of all vertices. (b) Compute betweenness centrality of all vertices. (c) Compute Freemans' Centralization value for degree and betweenness. (d) Define a centrality such that all four vertices at the corner have higher values.

(a) Compute degree centrality of all vertices. (b) Compute betweenness centrality of all vertices. (c) Compute Freemans' Centralization value for degree and betweenness. (d) Define a centrality such that all four vertices at the corner have higher values.

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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### Task Instructions

1. **Compute Degree Centrality of All Vertices**
Calculate the degree centrality for each vertex in the network.

2. **Compute Betweenness Centrality of All Vertices**
Determine the betweenness centrality for each vertex.

3. **Compute Freeman's Centralization Value for Degree and Betweenness**
Calculate Freeman's centralization measure for degree centrality and betweenness centrality.

4. **Define a Centrality Such That All Four Vertices at the Corner Have Higher Values**
Create or identify a centrality measure where the four corner vertices have higher rankings compared to others in the network.

### Diagram Description

- The diagram depicts a simple undirected graph in the shape of a rectangular grid with two rows and three columns.
- There are six vertices total, arranged in two horizontal rows with three vertices each.
- Each vertex is connected to its adjacent vertices horizontally and vertically but not diagonally.
- The vertices form two parallel lines, with connections forming a total of eight edges.

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