19.1.3. Adjacency Matrix

Try these first

1. 1.

   What does the entry A[i][j] represent in an adjacency matrix?

   Hint

   Remember the definition of adjacency matrix.

2. 2.

   Is the adjacency matrix symmetric for undirected graphs? Why?

   Hint

   Think about how the edges are defined.

3. 3.

   In an adjacency matrix, what does a value of 1 mean?

   • There is no edge
   • There is an edge
   • The vertex is isolated

   Hint

   Think about the purpose of the matrix.

4. 4.

   True or False: An adjacency matrix is always symmetric.

   • True
   • False

   Hint

   Reflect on what it means for edges to connect vertices.

5. 5.

   You have 8 vertices in a graph and 6 edges connecting them. Describe how you would create an adjacency matrix and what values you expect.

   Hint

   Visualize the connections between vertices to fill in the relevant edges.

6. 6.

   Design an algorithm to find if a path exists between two vertices using the adjacency matrix representation. What steps would you include?

   Hint

   Think about how breadth-first search would traverse neighbors in the matrix.