Explain why in a network with no loops or multiple edges, the maximum redundancy is

Chapter 7, Problem 46

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QUESTION:

Explain why in a network with no loops or multiple edges, the maximum redundancy is given by R = (N2 - 3N + 2) 2 . (Hint: The maximum redundancy occurs when the network is KN.)

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QUESTION:

Explain why in a network with no loops or multiple edges, the maximum redundancy is given by R = (N2 - 3N + 2) 2 . (Hint: The maximum redundancy occurs when the network is KN.)

ANSWER:

Step 1 of 2

The maximum redundancy occurs when we maximize the number of edges in a network. A simple graph of  vertices having exactly one edge between each pair of vertices is called a complete graph.

A complete graph of  vertices is denoted by , and the total number of edges are

with  vertices in complete graph.

We know that in a network with  vertices and  edges.

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