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Representing Graphs

Representing Graphs. Adjacency Matrix. Suppose we have a graph G with n nodes. The adjacency matrix is the n x n matrix A=[a ij ] with:. a ij = 1 if (i,j) is an edge a ij = 0 if (i,j) is not an edge. Good for dense graphs!. 0 1 1 1. 1 0 1 1. A =. 1 1 0 1. 1 1 1 0. Example.

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Representing Graphs

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  1. Representing Graphs

  2. Adjacency Matrix Suppose we have a graph G with n nodes. The adjacency matrix is the n x n matrix A=[aij] with: aij = 1 if (i,j) is an edge aij = 0 if (i,j) is not an edge Good for dense graphs!

  3. 0 1 1 1 1 0 1 1 A = 1 1 0 1 1 1 1 0 Example

  4. 0 1 1 1 0 1 1 1 3 2 2 2 1 0 1 1 1 0 1 1 2 3 2 2 1 1 0 1 1 1 0 1 2 2 3 2 1 1 1 0 1 1 1 0 2 2 2 3 Counting Paths The number of paths of length k from node i to node j is the entry in position (i,j) in the matrix Ak = A2 =

  5. Adjacency List Suppose we have a graph G with n nodes. The adjacency list is the list that contains all the nodes that each node is adjacent to Good for sparse graphs!

  6. 1 3 2 4 Example 1: 2,3 2: 1,3,4 3: 1,2,4 4: 2,3

  7. Simple graph Vertex = node Edge Degree Weight Neighbours Complete Dual Bipartite Planar Cycle Tree Path Circuit Components Spanning Tree Terms to know

  8. Adjacency Matrix and List • Definition • Useful for counting Here’s What You Need to Know…

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