(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)

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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Question

(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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