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Questions and Answers
What is a common way to store information about the connections of a graph?
What is a common way to store information about the connections of a graph?
- Adjacency matrix (correct)
- Dijkstra's Algorithm
- Distance matrix
- Minimum spanning tree
What is the purpose of Kruskal's Algorithm?
What is the purpose of Kruskal's Algorithm?
- To find the shortest path between two nodes
- To find the minimum spanning tree (correct)
- To raise a matrix to a power
- To store information about the connections of a graph
Raising an adjacency matrix to a power n gives the number of what?
Raising an adjacency matrix to a power n gives the number of what?
- Edges of weight n
- Walks of length n-1
- Walks of length n (correct)
- Nodes of degree n
What is the purpose of Dijkstra's Algorithm?
What is the purpose of Dijkstra's Algorithm?
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What is the main difference between Prim's Algorithm and Kruskal's Algorithm?
What is the main difference between Prim's Algorithm and Kruskal's Algorithm?
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Study Notes
Graphs
- A graph is a collection of points, called nodes or vertices, connected by lines called edges.
- Edges can have a weight and can be directed.
Graph Representation
- Graph information can be stored in a matrix, known as an adjacency matrix.
- Adjacency matrices store information about connections between nodes.
Matrix Operations
- Raising an adjacency matrix to a power n gives the number of walks of length n between any two nodes.
Distance Matrices
- Distance matrices record the weight of each edge between nodes.
Minimum Spanning Tree (MST)
- The MST is a subgraph that connects all nodes of a graph with the lowest total weight.
- MST can be found using Kruskal's Algorithm or Prim's Algorithm.
Kruskal's Algorithm
- Continually choose the lowest-weight edge that does not create a loop in the tree.
Prim's Algorithm
- Start at a random node and continually choose the lowest-weight edge that connects the tree to an unconnected node.
Shortest Path
- Dijkstra's Algorithm is used to find the shortest path between two nodes.
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