# MAT 2051 Unit 8 Discussion DQ1 Networking, Graphs, Adjacency Matrices, and Server Application

MAT 2051 Unit 8 Discussion DQ1 Networking, Graphs, Adjacency Matrices, and Server Application

Assume you are a network administrator of a large business firm that wishes to construct an intranet. Your firm has a number of computers, servers, and services such as printers, all connected to five hubs (hubs 1, 2, 3, 4, and 5), which must now be connected to each other. Assume each hub is separated by distances shown in the following adjacency matrix:

Each hub must be connected to at least one other hub, therefore, you only need to make four connections to allow communication between all computers. You can further minimize the cost of the cables and time by only connecting the closest hubs.

Consider and answer the following questions to evaluate this problem:

What is an intranet?

What is an adjacency matrix, and how do they relate to graphs?

What is the optimal connection of the five hubs that will minimize the length of the cable required to connect them? Note: The length of the cable will be the distance between the hubs as shown in the adjacency matrix.

How did you arrive at this answer? What algorithm should be used to solve this problem?

Hint: This is a graphical minimization problem. Make sure you comment on the following: What are the vertices? What are the weights on the edges? What are we trying to minimize?

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