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11.5 Examples on Matrix Representations

Following are examples on matrix representations and path segment. In these examples, we provide matrix representation corresponding to a given graph.

Example 1:
For a graphical representation:

Corresponding Relation Matrix and also, Connection Matrix representation is:

There is no path segment in this representation from node 1 to node 1.
Example 2:
For a graphical representation:

Corresponding Relationship Matrix Representation is:

And, the Connection Matrix is:

The path segment from node 1 to node 1 is a.
Alternatively, the path segment using link weights notation from node 1 to node 1 is a11.
Example 3:
For a graphical representation:

Corresponding Relationship Matrix representation is:

And, the Connection Matrix is:

The path segment from node 1 to node 2 is a.
Alternatively, the path segment using link weights notation from node 1 to node 2 is a22.
Example 4:
For a graphical representation:

One path segment from node 1 to node 7 is:

abcdf

Alternatively, the path segment using link weights notation from node 1 to node 7 is:

a12 a23 a35 a56 a67


Corresponding Relationship Matrix representation is:
And, the Connection Matrix is:
 
 
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