Completing a Table from a Network Diagram

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Question 1 of 4

1. Question
Fill in the table using the undirected network below

Fill in cells without values with $-$
- $\text(To)$
  
  $\text(From)$ A B C D E
  
  A $-$ (4) (7) (8) (7)
  
  B (4) $-$ (5) (-) (-)
  
  C (7) (5) $-$ (6) (-)
  
  D (8) (-) (6) $-$ (9)
  
  E (8) (-) (-) (9) $-$
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An undirected network has edges that goes both ways, so each edge’s value is used twice. It then forms a symmetrical table.

Fill up the table using the values of the edges going from a vertex to another.

Note that since this network is undirected, the values on the table will be symmetrical as well.

$\text(A to B)$ and $\text(B to A)=4$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $4$

$B$ $4$

$C$

$D$

$E$

$\text(A to C)$ and $\text(C to A)=7$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $4$ $7$

$B$ $4$

$C$ $7$

$D$

$E$

$\text(A to D)$ and $\text(D to A)=8$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $4$ $7$ $8$

$B$ $4$

$C$ $7$

$D$ $8$

$E$

$\text(A to E)$ and $\text(E to A)=7$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $4$ $7$ $8$ $7$

$B$ $4$

$C$ $7$

$D$ $8$

$E$ $7$

$\text(B to C)$ and $\text(C to B)=5$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $4$ $7$ $8$ $7$

$B$ $4$ $5$

$C$ $7$ $5$

$D$ $8$

$E$ $7$

$\text(C to D)$ and $\text(D to C)=6$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $4$ $7$ $8$ $7$

$B$ $4$ $5$

$C$ $7$ $5$ $6$

$D$ $8$ $6$

$E$ $7$

$\text(D to E)$ and $\text(E to D)=9$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $4$ $7$ $8$ $7$

$B$ $4$ $5$

$C$ $7$ $5$ $6$

$D$ $8$ $6$ $9$

$E$ $7$ $9$

All the values are listed, so simply add dashes ( $-$ ) to the rest of the cells.

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $-$ $4$ $7$ $8$ $7$

$B$ $4$ $-$ $5$ $-$ $-$

$C$ $7$ $5$ $-$ $6$ $-$

$D$ $8$ $-$ $6$ $-$ $9$

$E$ $7$ $-$ $-$ $9$ $-$

$\text(To)$

$\text(From)$ $A$ $B$ $C$ $D$ $E$

$A$ $-$ $4$ $7$ $8$ $7$

$B$ $4$ $-$ $5$ $-$ $-$

$C$ $7$ $5$ $-$ $6$ $-$

$D$ $8$ $-$ $6$ $-$ $9$

$E$ $7$ $-$ $-$ $9$ $-$

	$\text(To)$
$\text(From)$		A	B	C	D	E
A	$-$	(4)	(7)	(8)	(7)
B	(4)	$-$	(5)	(-)	(-)
C	(7)	(5)	$-$	(6)	(-)
D	(8)	(-)	(6)	$-$	(9)
E	(8)	(-)	(-)	(9)	$-$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$
$A$		$4$	$7$	$8$	$7$
$B$	$4$
$C$	$7$
$D$	$8$
$E$	$7$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$
$A$		$4$	$7$	$8$	$7$
$B$	$4$		$5$
$C$	$7$	$5$
$D$	$8$
$E$	$7$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$
$A$		$4$	$7$	$8$	$7$
$B$	$4$		$5$
$C$	$7$	$5$		$6$
$D$	$8$		$6$
$E$	$7$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$
$A$		$4$	$7$	$8$	$7$
$B$	$4$		$5$
$C$	$7$	$5$		$6$
$D$	$8$		$6$		$9$
$E$	$7$			$9$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$
$A$	$-$	$4$	$7$	$8$	$7$
$B$	$4$	$-$	$5$	$-$	$-$
$C$	$7$	$5$	$-$	$6$	$-$
$D$	$8$	$-$	$6$	$-$	$9$
$E$	$7$	$-$	$-$	$9$	$-$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$
$A$	$-$	$4$	$7$	$8$	$7$
$B$	$4$	$-$	$5$	$-$	$-$
$C$	$7$	$5$	$-$	$6$	$-$
$D$	$8$	$-$	$6$	$-$	$9$
$E$	$7$	$-$	$-$	$9$	$-$

Question 2 of 4

Fill in the table using the directed network below

Fill in cells without values with

$-$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$	$-$	(16)	(-)	(-)	(8)
	$Q$	(10)	$-$	(12)	(-)	(19)
	$R$	(-)	(-)	$-$	(15)	(-)
	$S$	(-)	(14)	(20)	$-$	(-)
	$T$	(10)	(-)	(-)	(13)	$-$

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A directed network has edges that only goes one way, meaning each edge’s value is used only once.

First, count the number of edges or connections the network has.

There are a total of

$10$ edges. Therefore, there will only be

$10$ values to be entered to the table.

Next, fill up the table using the values of the edges going from a vertex to another, following the given direction.

$\text(P to Q)=16$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$
	$Q$
	$R$
	$S$
	$T$

$\text(P to T)=8$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$
	$R$
	$S$
	$T$

$\text(Q to P)=10$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$
	$R$
	$S$
	$T$

$\text(Q to R)=12$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$		$12$
	$R$
	$S$
	$T$

$\text(Q to T)=19$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$		$12$		$19$
	$R$
	$S$
	$T$

$\text(R to S)=15$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$		$12$		$19$
	$R$				$15$
	$S$
	$T$

$\text(S to Q)=14$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$		$12$		$19$
	$R$				$15$
	$S$		$14$
	$T$

$\text(S to R)=20$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$		$12$		$19$
	$R$				$15$
	$S$		$14$	$20$
	$T$

$\text(T to P)=10$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$		$12$		$19$
	$R$				$15$
	$S$		$14$	$20$
	$T$	$10$

$\text(T to S)=13$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$		$16$			$8$
	$Q$	$10$		$12$		$19$
	$R$				$15$
	$S$		$14$	$20$
	$T$	$10$			$13$

Since there are already

$10$ values listed in the table, all the values are accounted for. Add dashes (

$-$ ) to the rest of the cells.

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$	$-$	$16$	$-$	$-$	$8$
	$Q$	$10$	$-$	$12$	$-$	$19$
	$R$	$-$	$-$	$-$	$15$	$-$
	$S$	$-$	$14$	$20$	$-$	$-$
	$T$	$10$	$-$	$-$	$13$	$-$

	$\text(To)$
$\text(From)$		$P$	$Q$	$R$	$S$	$T$
	$P$	$-$	$16$	$-$	$-$	$8$
	$Q$	$10$	$-$	$12$	$-$	$19$
	$R$	$-$	$-$	$-$	$15$	$-$
	$S$	$-$	$14$	$20$	$-$	$-$
	$T$	$10$	$-$	$-$	$13$	$-$

Question 3 of 4

Fill in the table using the directed network below

Fill in cells without values with

$-$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$	$-$	(-)	(-)	(-)	(10)	(2)
	$B$	(3)	$-$	(6)	(-)	(-)	(-)
	$C$	(-)	(8)	$-$	(7)	(-)	(-)
	$D$	(-)	(-)	(-)	$-$	(4)	(6)
	$E$	(-)	(-)	(12)	(-)	$-$	(5)
	$F$	(-)	(4)	(-)	(-)	(-)	$-$

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Mute

A directed network has edges that only goes one way, meaning each edge’s value is used only once.

First, count the number of edges or connections the network has.

There are a total of

$11$ edges. Therefore, there will only be

$11$ values to be entered to the table.

Next, fill up the table using the values of the edges going from a vertex to another, following the given direction.

$\text(A to E)=10$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$
	$B$
	$C$
	$D$
	$E$
	$F$

$\text(A to F)=2$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$
	$C$
	$D$
	$E$
	$F$

$\text(B to A)=3$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$
	$C$
	$D$
	$E$
	$F$

$\text(B to C)=6$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$
	$D$
	$E$
	$F$

$\text(C to B)=8$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$		$8$
	$D$
	$E$
	$F$

$\text(C to D)=7$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$		$8$		$7$
	$D$
	$E$
	$F$

$\text(D to E)=4$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$		$8$		$7$
	$D$					$4$
	$E$
	$F$

$\text(D to F)=6$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$		$8$		$7$
	$D$					$4$	$6$
	$E$
	$F$

$\text(E to C)=12$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$		$8$		$7$
	$D$					$4$	$6$
	$E$			$12$
	$F$

$\text(E to F)=5$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$		$8$		$7$
	$D$					$4$	$6$
	$E$			$12$			$5$
	$F$

$\text(F to B)=4$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$					$10$	$2$
	$B$	$3$		$6$
	$C$		$8$		$7$
	$D$					$4$	$6$
	$E$			$12$			$5$
	$F$		$4$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$	$-$	$-$	$-$	$-$	$10$	$2$
	$B$	$3$	$-$	$6$	$-$	$-$	$-$
	$C$	$-$	$8$	$-$	$7$	$-$	$-$
	$D$	$-$	$-$	$-$	$-$	$4$	$6$
	$E$	$-$	$-$	$12$	$-$	$-$	$5$
	$F$	$-$	$4$	$-$	$-$	$-$	$-$

Question 4 of 4

Fill in the table using the directed network below

Fill in cells without values with

$-$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$	$-$	(9)	(-)	(-)	(23)	(10)
	$B$	(8)	$-$	(-)	(-)	(-)	(15)
	$C$	(-)	(10)	$-$	(5)	(-)	(-)
	$D$	(-)	(-)	(-)	$-$	(8)	(7)
	$E$	(-)	(-)	(-)	(6)	$-$	(9)
	$F$	(-)	(14)	(6)	(-)	(-)	$-$

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Mute

A directed network has edges that only goes one way, meaning each edge’s value is used only once.

First, count the number of edges or connections the network has.

There are a total of

$13$ edges. Therefore, there will only be

$13$ values to be entered to the table.

Next, fill up the table using the values of the edges going from a vertex to another, following the given direction.

$\text(A to B)=9$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$
	$B$
	$C$
	$D$
	$E$
	$F$

$\text(A to E)=23$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$
	$B$
	$C$
	$D$
	$E$
	$F$

$\text(A to F)=10$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$
	$C$
	$D$
	$E$
	$F$

$\text(B to A)=8$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$
	$C$
	$D$
	$E$
	$F$

$\text(B to F)=15$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$
	$D$
	$E$
	$F$

$\text(C to B)=10$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$
	$D$
	$E$
	$F$

$\text(C to D)=5$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$		$5$
	$D$
	$E$
	$F$

$\text(D to E)=8$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$		$5$
	$D$					$8$
	$E$
	$F$

$\text(D to F)=7$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$		$5$
	$D$					$8$	$7$
	$E$
	$F$

$\text(E to D)=6$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$		$5$
	$D$					$8$	$7$
	$E$				$6$
	$F$

$\text(E to F)=9$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$		$5$
	$D$					$8$	$7$
	$E$				$6$		$9$
	$F$

$\text(F to B)=14$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$		$5$
	$D$					$8$	$7$
	$E$				$6$		$9$
	$F$		$14$

$\text(F to C)=6$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$		$9$			$23$	$10$
	$B$	$8$					$15$
	$C$		$10$		$5$
	$D$					$8$	$7$
	$E$				$6$		$9$
	$F$		$14$	$6$

	$\text(To)$
$\text(From)$		$A$	$B$	$C$	$D$	$E$	$F$
	$A$	$-$	$9$	$-$	$-$	$23$	$10$
	$B$	$8$	$-$	$-$	$-$	$-$	$15$
	$C$	$-$	$10$	$-$	$5$	$-$	$-$
	$D$	$-$	$-$	$-$	$-$	$8$	$7$
	$E$	$-$	$-$	$-$	$6$	$-$	$9$
	$F$	$-$	$14$	$6$	$-$	$-$	$-$

Completing a Table from a Network Diagram

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1. Question

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Keep Going!

2. Question

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Well Done!

3. Question

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Fantastic!

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