Show the adjacency matrix for the graph below? ### Understanding Graph Theory: Basic ConceptsThe image above represents a simple undirected graph, a foundational concept in graph theory.#### Components of the Graph1. **Vertices (Nodes)**: - The graph consists of six vertices, labeled A, B, C, D, E, and F. - Vertices are the fundamental units of the graph representing entities or points.2. **Edges (Connections)**: - **B** is connected to **A**, **C**, and **E**. - **C** is connected to **B**, **D**, and **F**. #### Understanding the Structure- **Vertex B** acts as a central node with three connections: to vertices A, C, and E.- **Vertex C** similarly acts as a central node connecting to vertices B, D, and F.- This graph is undirected, meaning the connections between vertices have no orientation; they go both ways.### Practical Applications in EducationGraphs like the one illustrated are used to teach various concepts:1. **Network Analysis**: - Helps in understanding the structure of networks, paths, and connectivity. 2. **Algorithmic Applications**: - Essential for learning algorithms related to searching (like Breadth-First Search and Depth-First Search) and pathfinding (like Dijkstra's Algorithm). 3. **Data Structures**: - Provides a graphical representation of data structures that are crucial for computer science and engineering studies.### ConclusionThe given image is an excellent example of a fundamental graph structure used in educational materials to help students understand basic concepts of graph theory, network analysis, and algorithmic design.

In adjacency matrix we need to create a matrix of size NxN Where N is the number of vertices in a…

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Engineering

Computer Science

B D

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Show the adjacency matrix for the graph below?

### Understanding Graph Theory: Basic Concepts

The image above represents a simple undirected graph, a foundational concept in graph theory.

#### Components of the Graph

1. **Vertices (Nodes)**:
- The graph consists of six vertices, labeled A, B, C, D, E, and F.
- Vertices are the fundamental units of the graph representing entities or points.

2. **Edges (Connections)**:
- **B** is connected to **A**, **C**, and **E**.
- **C** is connected to **B**, **D**, and **F**.

#### Understanding the Structure

- **Vertex B** acts as a central node with three connections: to vertices A, C, and E.
- **Vertex C** similarly acts as a central node connecting to vertices B, D, and F.
- This graph is undirected, meaning the connections between vertices have no orientation; they go both ways.

### Practical Applications in Education

Graphs like the one illustrated are used to teach various concepts:

1. **Network Analysis**:
- Helps in understanding the structure of networks, paths, and connectivity.

2. **Algorithmic Applications**:
- Essential for learning algorithms related to searching (like Breadth-First Search and Depth-First Search) and pathfinding (like Dijkstra's Algorithm).

3. **Data Structures**:
- Provides a graphical representation of data structures that are crucial for computer science and engineering studies.

### Conclusion

The given image is an excellent example of a fundamental graph structure used in educational materials to help students understand basic concepts of graph theory, network analysis, and algorithmic design.

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