Drawing a Network 1

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Precalculus

Networks

Drawing a Network

Drawing a Network 1

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Question 1 of 4

1. Question
Which diagram represents the given map below?
- 1.
- 2.
- 3.
- 4.
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Properties of the given map:

$1 .$ $1.$ Vertex $A$ $A$ is connected to vertices $B$ $B$ , $D$ $D$ , and $E$ $E$ .

$2 .$ $2.$ Vertex $B$ $B$ is connected to vertices $A$ $A$ and $C$ $C$ .

$3 .$ $3.$ Vertex $C$ $C$ is connected to vertices $B$ $B$ , $D$ $D$ , and $E$ $E$ .

$4 .$ $4.$ Vertex $D$ $D$ is connected to vertices $A$ $A$ and $E$ $E$ .

$5 .$ $5.$ There are $2$ $2$ edges connecting vertices $A$ $A$ and $D$ $D$ .

Check each diagrams to see if their network has the above properties.

$1$ $1$ st Figure

Notice that vertices $D$ $D$ and $E$ $E$ are not connected.

Therefore, the first diagram does not represent the given map.

$2$ $2$ nd Figure

Notice that there is only one edge connecting the vertices $A$ $A$ and $D$ $D$ .

Therefore, the second diagram does not represent the given map.

$3$ $3$ rd Figure

This diagram fits all the properties of the given map.

Therefore, the third diagram represents the given map.

$4$ $4$ th Figure

Notice that there is only one edge connecting the vertices $A$ $A$ and $D$ $D$ .

Therefore, the fourth diagram does not represent the given map.

Therefore, the third diagram is the diagram representing the given map.
Question 2 of 4

2. Question
The diagram below show how to get to each town. Find out the best way to travel from town $U$ $U$ to town $Z$ $Z$ .
- 1. $U - X - Y - Z$ $U-X-Y-Z$
- 2. $U - W - Y - Z$ $U-W-Y-Z$
- 3. $U - W - X - Z$ $U-W-X-Z$
- 4. $U - V - X - Z$ $U-V-X-Z$
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A directed network has edges that only goes one way, meaning each edge’s value is used only once.

Check which edges will head to town $Z$ $Z$ from town $U$ $U$ . Remember that we can only move to the direction of the arrow.

First, we can move directly to town $X$ $X$ from town $U$ $U$ .

Next, we can move directly to town $Y$ $Y$ from town $X$ $X$ .

Finally, we can move directly to town $Z$ $Z$ from town $Y$ $Y$ .

This means that the best path is $U - X - Y - Z$ $U-X-Y-Z$ .

Therefore, the best path to use when heading from town $U$ $U$ to town $Z$ $Z$ is $U - X - Y - Z$ $U-X-Y-Z$
Question 3 of 4

3. Question
Which of the following networks illustrate the table below?
- 1.
- 2.
- 3.
- 4.
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There is more than one way to draw a network diagram, depending on its connections.

First, identify which vertex has the most degrees.

Degrees are indicated by $1$ $1$ in the table.

Since the table shows that $B$ $B$ has the most cells marked with $1$ $1$ , vertex $B$ $B$ has the most degrees, which is $4$ $4$ .

You can start the diagram by adding a point for $B$ $B$ .

Next, identify which vertex has the second most degrees.

Since the table shows that $E$ $E$ has $3$ $3$ cells marked with $1$ $1$ , vertex $E$ $E$ has the second most degrees, which is $3$ $3$ .

You can plot a point for $E$ $E$ on the diagram as well.

Now take note that this table is not directed, which means that the values on the table are symmetrical.

This also means that there will be two connections for each edge that we draw.

Now we can start adding the rest of the vertices and adding edges from one vertex to another using the table as reference.

Remember that networks can be drawn in more than one way. Here is one illustration of this network:

Vertex $A$ $A$ is connected to vertex $B$ $B$

Vertex $C$ $C$ is connected to vertex $B$ $B$ and $E$ $E$

Vertex $D$ $D$ is connected to vertex $B$ $B$ and $E$ $E$

Vertices $B$ $B$ and $E$ $E$ are also connected

As mentioned earlier, this is just one way to illustrate this table as a network. Another correct illustration would be this network:
Question 4 of 4

4. Question
Which of the following networks illustrate the table below?
- 1.
- 2.
- 3.
- 4.
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There is more than one way to draw a network diagram, depending on its connections.

First, identify which vertex has the most degrees.

Degrees are indicated by how many cells with values a column or a row has.

Since the table shows that $F$ $F$ has the most cells with values, vertex $F$ $F$ has the most degrees, which is $5$ $5$ .

You can start the diagram by adding a point for $F$ $F$ .

Next, notice that $F$ $F$ has values for all the other vertices in the table. This means that $F$ $F$ should be connected to all the other vertices. One way to illustrate it is:

Now take note that this table is not directed, which means that the values on the table are symmetrical.

This also means that there will be two connections for each edge that we draw.

Now we can start adding the rest of the vertices and adding edges from one vertex to another using the table as reference.

Remember that networks can be drawn in more than one way. Here is one illustration of this network:

Vertex $A$ $A$ is connected to vertex $B$ $B$ with a value of $20$ $20$ .

Vertex $A$ $A$ is connected to vertex $E$ $E$ with a value of $30$ $30$

The edge connecting vertex $A$ $A$ and vertex $F$ $F$ has a value of $18$ $18$

Vertex $B$ $B$ is connected to vertex $C$ $C$ with a value of $35$ $35$

The edge connecting vertex $B$ $B$ and vertex $F$ $F$ has a value of $15$ $15$

Vertex $C$ $C$ is connected to vertex $D$ $D$ with a value of $22$ $22$

Vertex $C$ $C$ is connected to vertex $F$ $F$ with a value of $30$ $30$

Vertex $D$ $D$ is connected to vertex $E$ $E$ with a value of $20$ $20$

The edge connecting vertex $D$ $D$ and vertex $F$ $F$ has a value of $45$ $45$

The edge connecting vertex $E$ $E$ and vertex $F$ $F$ has a value of $32$ $32$

Drawing a Network 1

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Quiz summary

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1. Question

Hint

Nice Job!

Properties of the given map:

2. Question

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Excellent!

3. Question

Hint

Fantastic!

4. Question

Hint

Keep Going!

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