19.1.2. Graph Representation

Try these first

1. 1.

   Define what a graph is.

   Hint

   Think about how they are used to represent relationships.

2. 2.

   What does an entry of '1' in an adjacency matrix indicate?

   Hint

   Refer back to how edges are represented.

3. 3.

   What does an adjacency list do?

   • Stores all edges
   • Stores neighbors for each vertex
   • Stores vertex counts

   Hint

   Remember, adjacency lists focus on connections!

4. 4.

   True or False: An adjacency matrix is preferable for very sparse graphs.

   • True
   • False

   Hint

   Think about what 'sparse' means in the context of edges.

5. 5.

   Given the following adjacency matrix, write the corresponding adjacency list.

   Hint

   Remember to look at each row and note neighbors.

6. 6.

   Design an algorithm that utilizes breadth-first search to determine if a path exists from vertex A to vertex B in a graph.

   Hint

   Consider how to track visited vertices to avoid cycles.