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(Paths in Graphs) Graph theory studies sets of vertices connect by edges. A very simple way to store the connectivity information about a graph is using what is called an adjacency malrir. In an adjacency matrix A, entry aij is 1 if nodes i and j are connected by an edge and is 0 otherwise. For example, the graph below has adjacency matrix [0 1 1 0 1010 A = 1 10 1 lo o 1 0 2. 3 One interesting calculation that can casily be done using an adjacency matrix is that we can count the number of paths between two nodes in the graph by calculating powers of the matrix. For example, because [2 1 1 1] A - ! 2 1 1 1 13 0j 10 1] we know that there are 0 paths of length 2 from node 3 to node 4 because the entry in row 3, column 4 of A° is a 0. find_num_paths Function: Input parameters: • a square adjacency matrix •a scalar representing the desired path length • two scalars representing the two nodes Output parameters: • a scalar representing the number of paths connecting the two desired nodes of the desired length A possible sample case is: > num_paths = find_num_paths ([ 0 110; 10 10; 1 101 ; 0010 ], 2, 3, 4) num_paths =

(Paths in Graphs) Graph theory studies sets of vertices connect by edges. A very simple way to store the connectivity information about a graph is using what is called an adjacency malrir. In an adjacency matrix A, entry aij is 1 if nodes i and j are connected by an edge and is 0 otherwise. For example, the graph below has adjacency matrix [0 1 1 0 1010 A = 1 10 1 lo o 1 0 2. 3 One interesting calculation that can casily be done using an adjacency matrix is that we can count the number of paths between two nodes in the graph by calculating powers of the matrix. For example, because [2 1 1 1] A - ! 2 1 1 1 13 0j 10 1] we know that there are 0 paths of length 2 from node 3 to node 4 because the entry in row 3, column 4 of A° is a 0. find_num_paths Function: Input parameters: • a square adjacency matrix •a scalar representing the desired path length • two scalars representing the two nodes Output parameters: • a scalar representing the number of paths connecting the two desired nodes of the desired length A possible sample case is: > num_paths = find_num_paths ([ 0 110; 10 10; 1 101 ; 0010 ], 2, 3, 4) num_paths =

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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(Paths in Graphs) Graph theory studies sets of vertices connect by edges. A very simple way to store the connectivity information about a graph is using what is called an adjacency malrir. In an adjacency matrix A, entry aij is 1 if nodes i and j are connected by an edge and is 0 otherwise. For example, the graph below has adjacency matrix [0 1 1 01 101 0 A = 1 10 1 o o 10 3 One interesting calculation that can casily be done using an adjacency matrix is that we can count the number of paths between two nodes in the graph by calculating powers of the matrix. For example, because 1 11] 1 2 1 1 1 1 3 0 1 10 1 we know that there are 0 paths of length 2 from node 3 to node 4 because the entry in row 3, column 4 of A is a 0. find num_paths Function: Input parameters: • a square adjacency matrix • a scalar representing the desired path length • two scalars representing the two nodes Output parameters: • a scalar representing the number of paths connecting the two desired nodes of the desired length A possible sample case is: > num_paths = find_num_paths ([ 0 110 ; 10 10; 1 10 1 ; 0010 ], 2, 3, 4) num_paths =
Transcribed Image Text:(Paths in Graphs) Graph theory studies sets of vertices connect by edges. A very simple way to store the connectivity information about a graph is using what is called an adjacency malrir. In an adjacency matrix A, entry aij is 1 if nodes i and j are connected by an edge and is 0 otherwise. For example, the graph below has adjacency matrix [0 1 1 01 101 0 A = 1 10 1 o o 10 3 One interesting calculation that can casily be done using an adjacency matrix is that we can count the number of paths between two nodes in the graph by calculating powers of the matrix. For example, because 1 11] 1 2 1 1 1 1 3 0 1 10 1 we know that there are 0 paths of length 2 from node 3 to node 4 because the entry in row 3, column 4 of A is a 0. find num_paths Function: Input parameters: • a square adjacency matrix • a scalar representing the desired path length • two scalars representing the two nodes Output parameters: • a scalar representing the number of paths connecting the two desired nodes of the desired length A possible sample case is: > num_paths = find_num_paths ([ 0 110 ; 10 10; 1 10 1 ; 0010 ], 2, 3, 4) num_paths =
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