The Win/Loss Record in a Directed Graph
Directed graphs are ways to represent relationships between many different objects. They can be used
to show the outcomes of competitive games between two teams. We will look at the outcomes of the
first six weeks of the American Football Conference represented as a directed graph. Each arrow
represents a game played in the first six weeks. The tail of the arrow is at the loser of the game. The
head of the arrow is at the winner of the game.
1) What teams have the Texans played?
2) Who have the Browns lost games to?
3) What is the record of each team?
4) A cycle is a sequence of arrows that start and end in the same place. Are
there any cycles in the above graph? What are they?
Use the following data for NFC games to make a directed graph for the teams
: Dallas Cowboys, NY Giants, Philadelphia Eagles, Washington Redskins,
Chicago Bears, Detroit Lions, Green Bay Packers, and MIN Vikings
Week 1
NYG
PHI
CHI
DET
GB
MIN
Week 5
NYG
PHI
CHI
GBP
MIN
14
31
30
27
42
17
25
24
13
25
34
WAS
STL
ATL
TBB
NOS
SDC
SEA
BUF
DET
ATL
ARI
28
13
12
20
34
24
36
31
24
14
10
Week 2
DAL
NYG
PHI
WAS
CHI
DET
GB
MIN
Week 6
DAL
NYG
PHI
CHI
DET
GBP
27
28
31
22
12
48
30
20
16
27
20
39
19
24
SFO
STL
ATL
ARI
NOS
KCC
CAR
TBB
NEW
BUF
WAS
MIN
SFO
STL
24
16
35
21
30
3
23
24
20
24
13
10
25
3
Week 3
DAL
NYG
CHI
DET
18
29
17
26
WAS
PHI
GBP
MIN
16
16
27
23
Week 7
DAL
WAS
CHI
DET
GBP
34
20
24
16
33
STL
CAR
TBB
ATL
MIN
7
33
18
23
27
Week 4
DAL
NYG
PHI
WAS
CHI
GB
MIN
30
31
23
17
34
49
17
DET
ARI
SFO
STL
CAR
DEN
KCC
34
27
24
10
29
23
22