IowaHawkBlog's Degrees of Separation Ranking - Week 12

In this system, a team's rank is based solely on who they have defeated, and who those teams have defeated, and who those teams have defeated, down 5 levels.   I think the easiest way to explain this is with an example.  Let's say Team A defeated Team B and Team C.  Team A will get 5 points for each of those wins.  Let's then assume Team B has beaten D and E while C has only beaten F.  While B and C will get their points for those respective wins, Team A will also get 4 points for each of those three "Linked Wins."  This process continues down to give 3 points, and 2 points, and 1 point for each successive "Degree of Separation" of the linked wins. 

That's it. Teams can't get points for a linked win over themselves, and can only get credit for each of the other FBS teams once---at whatever the fewest degrees of separation is that gives them that linked win.

We have played around with what weights to use for each win at each degree of separation.  In the example above I used {5,4,3,2,1} for the weights at each degree, but below I am also including rankings based on other weight vectors.  First though, the linear one using {5,4,3,2,1}:

Rank	Team	W	L	Conf	Linked Wins	Score
1	LSU	10	0	SEC	119	370
2	Georgia	9	1	SEC	121	357
3	Michigan	8	2	B10	118	351
4	Penn State	9	1	B10	121	345
5	Wisconsin	8	2	B10	119	337
6	Florida	9	2	SEC	120	335
7	Ohio State	10	0	B10	118	331
8	Notre Dame	8	2	IND	111	324
9	BYU	6	4	IND	117	323
10	Minnesota	9	1	B10	119	319
11	SMU	9	1	AAC	114	319
12	Auburn	7	3	SEC	114	316
13	Boise State	9	1	MWC	112	313
14	Cincinnati	9	1	AAC	108	305
15	Clemson	11	0	ACC	109	305
16	Iowa	7	3	B10	114	305
17	Oklahoma St.	7	3	B12	114	301
18	Toledo	6	4	MID	114	291
19	Utah	9	1	PAC	109	289
20	Pittsburgh	7	3	ACC	112	284
21	App. St.	9	1	SUN	108	283
22	Memphis	9	1	AAC	109	282
23	Kansas St.	6	4	B12	109	278
24	Oklahoma	9	1	B12	107	278
25	Temple	7	3	AAC	109	277
26	UCF	7	3	AAC	109	276
27	Texas	6	4	B12	109	273
28	Wake Forest	7	3	ACC	106	273
29	Alabama	9	1	SEC	108	271
30	Kentucky	5	5	SEC	119	271
31	Wash.	6	4	PAC	111	270
32	Baylor	9	1	B12	106	269
33	USC	7	4	PAC	105	267
34	Miami (FL)	6	4	ACC	106	266
35	Oregon	9	1	PAC	102	264
36	S. Carolina	4	7	SEC	114	263
37	Illinois	6	4	B10	113	262
38	Tulsa	3	7	AAC	106	250
39	Navy	7	2	AAC	102	249
40	N. Carolina	4	6	ACC	108	248
41	Virginia	7	3	ACC	105	248
42	Buffalo	5	5	MID	108	247
43	Mich. St.	4	6	B10	101	247
44	Tennessee	5	5	SEC	113	246
45	Louisville	6	4	ACC	98	245
46	Virginia Tech	7	3	ACC	105	245
47	Miss. St.	4	6	SEC	106	244
48	Missouri	5	5	SEC	110	242
49	Arizona St.	5	5	PAC	97	241
50	E. Mich.	5	5	MID	101	233
51	Texas A&M	7	3	SEC	103	230
52	TCU	5	5	B12	104	229
53	Florida St.	6	5	ACC	91	228
54	Iowa State	6	4	B12	97	227
55	Air Force	8	2	MWC	92	226
56	Colorado	4	6	PAC	96	226
57	San Diego St.	8	2	MWC	93	225
58	W. Virginia	4	6	B12	101	225
59	W. Michigan	7	4	MID	101	224
60	S. Florida	4	6	AAC	102	223
61	California	5	5	PAC	92	222
62	Oregon St.	5	5	PAC	99	221
63	Georgia Tech	2	8	ACC	101	220
64	Wyoming	6	4	MWC	97	219
65	Ball State	4	6	MID	103	217
66	UL Lafayette	8	2	SUN	93	215
67	Hawaii	7	4	MWC	89	214
68	Stanford	4	6	PAC	96	214
69	UCLA	4	6	PAC	94	211
70	Syracuse	4	6	ACC	91	210
71	Texas Tech	4	6	B12	100	208
72	Georgia St.	6	4	SUN	90	205
73	BC	5	5	ACC	89	203
74	Georgia So.	6	4	SUN	88	200
75	N. Illinois	4	6	MID	99	198
76	Nebraska	4	6	B10	96	197
77	Arizona	4	6	PAC	91	196
78	Utah State	6	4	MWC	86	195
79	Kansas	3	7	B12	99	193
80	Wash. St.	5	5	PAC	88	193
81	Vanderbilt	2	8	SEC	101	192
82	Duke	4	6	ACC	89	191
83	Nevada	6	4	MWC	82	190
84	Indiana	7	3	B10	88	189
85	Miami (OH)	6	4	MID	93	184
86	NC State	4	6	ACC	93	184
87	Bowling Grn	3	7	MID	94	181
88	C. Mich.	7	4	MID	88	180
89	Florida Atl.	7	3	USA	81	180
90	Ohio	4	6	MID	93	180
91	Purdue	4	6	B10	84	178
92	Kent State	4	6	MID	93	176
93	Tulane	6	4	AAC	80	176
94	Marshall	7	3	USA	70	172
95	LA Tech	8	2	USA	75	166
96	Liberty	6	4	IND	77	153
97	Coastal Caro.	4	6	SUN	76	149
98	Fresno St.	4	6	MWC	68	144
99	Arkansas St.	6	4	SUN	63	139
100	Troy	5	5	SUN	64	131
101	Maryland	3	7	B10	67	130
102	UL Monroe	4	6	SUN	57	121
103	Texas State	3	7	SUN	57	119
104	S. Miss.	7	3	USA	48	117
105	Ole Miss	4	7	SEC	59	113
106	Mid. Tenn.	3	7	USA	46	110
107	Colorado St.	4	6	MWC	56	106
108	W. Kentucky	6	4	USA	36	101
109	UNLV	2	8	MWC	54	95
110	Rutgers	2	8	B10	44	82
111	Charlotte	5	5	USA	30	78
112	North Texas	4	6	USA	30	75
113	San Jose St.	4	6	MWC	28	71
114	Rice	1	9	USA	30	66
115	UAB	7	3	USA	23	60
116	Houston	3	7	AAC	24	59
117	Florida Int.	5	5	USA	22	56
118	Army	5	6	IND	22	55
119	Arkansas	2	8	SEC	29	54
120	Northwestern	2	8	B10	29	53
121	UTSA	4	6	USA	22	47
122	Connecticut	2	8	AAC	2	9
123	E. Carolina	3	7	AAC	1	5
124	UMASS	1	10	MID	1	5
125	New Mexico	2	8	MWC	1	5
126	Akron	0	10	MID	0	0
127	NM St.	1	9	IND	0	0
128	Old Dominion	1	9	USA	0	0
129	S. Alabama	1	9	SUN	0	0
130	UTEP	1	9	USA	0	0

Here is the rankings using weights of {256,16,4,2,1}:

Rank	Team	W	L	Conf	Linked Wins	Score
1	Ohio State	10	0	B10	118	3216
2	Clemson	11	0	ACC	109	3134
3	LSU	10	0	SEC	119	3041
4	SMU	9	1	AAC	114	2885
5	Cincinnati	9	1	AAC	108	2841
6	Georgia	9	1	SEC	121	2737
7	Alabama	9	1	SEC	108	2735
8	Michigan	8	2	B10	118	2718
9	Notre Dame	8	2	IND	111	2694
10	Penn State	9	1	B10	121	2694
11	Wisconsin	8	2	B10	119	2691
12	Boise State	9	1	MWC	112	2645
13	Minnesota	9	1	B10	119	2623
14	App. St.	9	1	SUN	108	2549
15	Utah	9	1	PAC	109	2545
16	Memphis	9	1	AAC	109	2535
17	Oregon	9	1	PAC	102	2533
18	Oklahoma	9	1	B12	107	2505
19	Baylor	9	1	B12	106	2461
20	Auburn	7	3	SEC	114	2412
21	Florida	9	2	SEC	120	2367
22	Iowa	7	3	B10	114	2359
23	USC	7	4	PAC	105	2254
24	Air Force	8	2	MWC	92	2182
25	San Diego St.	8	2	MWC	93	2147
26	UL Lafayette	8	2	SUN	93	2131
27	Oklahoma St.	7	3	B12	114	2038
28	LA Tech	8	2	USA	75	2028
29	Pittsburgh	7	3	ACC	112	2014
30	UCF	7	3	AAC	109	2014
31	Wake Forest	7	3	ACC	106	2012
32	Texas	6	4	B12	109	1998
33	Temple	7	3	AAC	109	1992
34	Illinois	6	4	B10	113	1960
35	Navy	7	2	AAC	102	1948
36	Virginia	7	3	ACC	105	1922
37	BYU	6	4	IND	117	1918
38	Texas A&M	7	3	SEC	103	1901
39	W. Michigan	7	4	MID	101	1891
40	Hawaii	7	4	MWC	89	1884
41	Marshall	7	3	USA	70	1856
42	Florida Atl.	7	3	USA	81	1818
43	Indiana	7	3	B10	88	1818
44	Toledo	6	4	MID	114	1794
45	Miami (FL)	6	4	ACC	106	1765
46	C. Mich.	7	4	MID	88	1760
47	Kansas St.	6	4	B12	109	1748
48	Wash.	6	4	PAC	111	1745
49	Louisville	6	4	ACC	98	1739
50	W. Kentucky	6	4	USA	36	1719
51	S. Miss.	7	3	USA	48	1702
52	Kentucky	5	5	SEC	119	1699
53	Virginia Tech	7	3	ACC	105	1668
54	Florida St.	6	5	ACC	91	1667
55	Georgia St.	6	4	SUN	90	1643
56	Iowa State	6	4	B12	97	1637
57	Wyoming	6	4	MWC	97	1637
58	Nevada	6	4	MWC	82	1604
59	Utah State	6	4	MWC	86	1588
60	Georgia So.	6	4	SUN	88	1580
61	UAB	7	3	USA	23	1580
62	Tulane	6	4	AAC	80	1563
63	Miami (OH)	6	4	MID	93	1523
64	Arkansas St.	6	4	SUN	63	1486
65	Miss. St.	4	6	SEC	106	1486
66	Mich. St.	4	6	B10	101	1458
67	Arizona St.	5	5	PAC	97	1441
68	Tennessee	5	5	SEC	113	1438
69	Buffalo	5	5	MID	108	1432
70	E. Mich.	5	5	MID	101	1428
71	Colorado	4	6	PAC	96	1421
72	California	5	5	PAC	92	1417
73	Missouri	5	5	SEC	110	1412
74	N. Carolina	4	6	ACC	108	1412
75	TCU	5	5	B12	104	1385
76	UCLA	4	6	PAC	94	1367
77	BC	5	5	ACC	89	1360
78	Stanford	4	6	PAC	96	1359
79	Oregon St.	5	5	PAC	99	1354
80	Nebraska	4	6	B10	96	1337
81	Wash. St.	5	5	PAC	88	1323
82	Purdue	4	6	B10	84	1291
83	Liberty	6	4	IND	77	1217
84	Troy	5	5	SUN	64	1204
85	Tulsa	3	7	AAC	106	1190
86	S. Carolina	4	7	SEC	114	1164
87	Syracuse	4	6	ACC	91	1137
88	Charlotte	5	5	USA	30	1136
89	W. Virginia	4	6	B12	101	1108
90	Florida Int.	5	5	USA	22	1098
91	Ball State	4	6	MID	103	1087
92	S. Florida	4	6	AAC	102	1085
93	Arizona	4	6	PAC	91	1065
94	Texas Tech	4	6	B12	100	1062
95	N. Illinois	4	6	MID	99	1050
96	Duke	4	6	ACC	89	1048
97	NC State	4	6	ACC	93	1039
98	Ohio	4	6	MID	93	1029
99	Kent State	4	6	MID	93	991
100	Coastal Caro.	4	6	SUN	76	985
101	Fresno St.	4	6	MWC	68	981
102	UL Monroe	4	6	SUN	57	945
103	Ole Miss	4	7	SEC	59	911
104	Colorado St.	4	6	MWC	56	901
105	San Jose St.	4	6	MWC	28	890
106	North Texas	4	6	USA	30	882
107	Army	5	6	IND	22	858
108	Georgia Tech	2	8	ACC	101	841
109	UTSA	4	6	USA	22	814
110	Kansas	3	7	B12	99	795
111	Vanderbilt	2	8	SEC	101	795
112	Bowling Grn	3	7	MID	94	759
113	Mid. Tenn.	3	7	USA	46	730
114	Maryland	3	7	B10	67	693
115	Texas State	3	7	SUN	57	693
116	Rutgers	2	8	B10	44	635
117	Houston	3	7	AAC	24	614
118	Northwestern	2	8	B10	29	581
119	UNLV	2	8	MWC	54	377
120	Rice	1	9	USA	30	349
121	Arkansas	2	8	SEC	29	344
122	Connecticut	2	8	AAC	2	272
123	E. Carolina	3	7	AAC	1	256
124	UMASS	1	10	MID	1	256
125	New Mexico	2	8	MWC	1	256
126	Akron	0	10	MID	0	0
127	NM St.	1	9	IND	0	0
128	Old Dominion	1	9	USA	0	0
129	S. Alabama	1	9	SUN	0	0
130	UTEP	1	9	USA	0	0

Here is the rankings using weights of {1000,100,10,1,0}:

Rank	Team	W	L	Conf	Linked Wins	Score
1	Ohio State	10	0	B10	118	13202
2	Clemson	11	0	ACC	109	12732
3	LSU	10	0	SEC	119	12541
4	SMU	9	1	AAC	114	11648
5	Cincinnati	9	1	AAC	108	11397
6	Georgia	9	1	SEC	121	11207
7	Notre Dame	8	2	IND	111	11104
8	Michigan	8	2	B10	118	11099
9	Wisconsin	8	2	B10	119	10980
10	Penn State	9	1	B10	121	10945
11	Boise State	9	1	MWC	112	10785
12	Alabama	9	1	SEC	108	10782
13	Minnesota	9	1	B10	119	10558
14	Oregon	9	1	PAC	102	10238
15	App. St.	9	1	SUN	108	10226
16	Utah	9	1	PAC	109	10150
17	Memphis	9	1	AAC	109	10119
18	Auburn	7	3	SEC	114	9911
19	Oklahoma	9	1	B12	107	9907
20	Baylor	9	1	B12	106	9616
21	Iowa	7	3	B10	114	9561
22	Florida	9	2	SEC	120	9406
23	USC	7	4	PAC	105	8991
24	Air Force	8	2	MWC	92	8713
25	San Diego St.	8	2	MWC	93	8436
26	UL Lafayette	8	2	SUN	93	8378
27	Oklahoma St.	7	3	B12	114	8027
28	Wake Forest	7	3	ACC	106	8024
29	UCF	7	3	AAC	109	8016
30	Pittsburgh	7	3	ACC	112	7956
31	BYU	6	4	IND	117	7931
32	LA Tech	8	2	USA	75	7911
33	Texas	6	4	B12	109	7908
34	Temple	7	3	AAC	109	7831
35	Navy	7	2	AAC	102	7681
36	Illinois	6	4	B10	113	7675
37	Marshall	7	3	USA	70	7516
38	Virginia	7	3	ACC	105	7475
39	Texas A&M	7	3	SEC	103	7435
40	Hawaii	7	4	MWC	89	7425
41	W. Michigan	7	4	MID	101	7399
42	Toledo	6	4	MID	114	7159
43	Florida Atl.	7	3	USA	81	7141
44	Miami (FL)	6	4	ACC	106	7110
45	Indiana	7	3	B10	88	7070
46	Louisville	6	4	ACC	98	7057
47	W. Kentucky	6	4	USA	36	6946
48	Wash.	6	4	PAC	111	6915
49	Kansas St.	6	4	B12	109	6884
50	S. Miss.	7	3	USA	48	6683
51	C. Mich.	7	4	MID	88	6665
52	Florida St.	6	5	ACC	91	6602
53	Georgia St.	6	4	SUN	90	6573
54	Kentucky	5	5	SEC	119	6528
55	Virginia Tech	7	3	ACC	105	6476
56	Wyoming	6	4	MWC	97	6418
57	Nevada	6	4	MWC	82	6372
58	Iowa State	6	4	B12	97	6361
59	Utah State	6	4	MWC	86	6203
60	Tulane	6	4	AAC	80	6142
61	UAB	7	3	USA	23	6126
62	Georgia So.	6	4	SUN	88	6101
63	Miss. St.	4	6	SEC	106	6044
64	Mich. St.	4	6	B10	101	5801
65	Arkansas St.	6	4	SUN	63	5799
66	Miami (OH)	6	4	MID	93	5749
67	Arizona St.	5	5	PAC	97	5710
68	E. Mich.	5	5	MID	101	5658
69	California	5	5	PAC	92	5656
70	Colorado	4	6	PAC	96	5656
71	Tennessee	5	5	SEC	113	5635
72	Buffalo	5	5	MID	108	5584
73	Missouri	5	5	SEC	110	5456
74	N. Carolina	4	6	ACC	108	5415
75	TCU	5	5	B12	104	5336
76	BC	5	5	ACC	89	5333
77	UCLA	4	6	PAC	94	5328
78	Stanford	4	6	PAC	96	5240
79	Nebraska	4	6	B10	96	5183
80	Oregon St.	5	5	PAC	99	5147
81	Wash. St.	5	5	PAC	88	5106
82	Purdue	4	6	B10	84	4958
83	Tulsa	3	7	AAC	106	4641
84	Troy	5	5	SUN	64	4608
85	Liberty	6	4	IND	77	4544
86	Syracuse	4	6	ACC	91	4512
87	Charlotte	5	5	USA	30	4468
88	S. Carolina	4	7	SEC	114	4331
89	Florida Int.	5	5	USA	22	4325
90	W. Virginia	4	6	B12	101	4161
91	Ball State	4	6	MID	103	4046
92	Arizona	4	6	PAC	91	4029
93	S. Florida	4	6	AAC	102	3988
94	Duke	4	6	ACC	89	3929
95	Texas Tech	4	6	B12	100	3911
96	NC State	4	6	ACC	93	3902
97	N. Illinois	4	6	MID	99	3886
98	Ohio	4	6	MID	93	3850
99	Fresno St.	4	6	MWC	68	3742
100	Coastal Caro.	4	6	SUN	76	3731
101	UL Monroe	4	6	SUN	57	3625
102	Kent State	4	6	MID	93	3571
103	San Jose St.	4	6	MWC	28	3564
104	North Texas	4	6	USA	30	3469
105	Army	5	6	IND	22	3425
106	Ole Miss	4	7	SEC	59	3405
107	Colorado St.	4	6	MWC	56	3377
108	UTSA	4	6	USA	22	3126
109	Georgia Tech	2	8	ACC	101	3071
110	Mid. Tenn.	3	7	USA	46	3009
111	Vanderbilt	2	8	SEC	101	2898
112	Kansas	3	7	B12	99	2893
113	Bowling Grn	3	7	MID	94	2692
114	Texas State	3	7	SUN	57	2635
115	Maryland	3	7	B10	67	2547
116	Houston	3	7	AAC	24	2455
117	Rutgers	2	8	B10	44	2442
118	Northwestern	2	8	B10	29	2226
119	Arkansas	2	8	SEC	29	1336
120	Rice	1	9	USA	30	1290
121	UNLV	2	8	MWC	54	1287
122	Connecticut	2	8	AAC	2	1100
123	E. Carolina	3	7	AAC	1	1000
124	UMASS	1	10	MID	1	1000
125	New Mexico	2	8	MWC	1	1000
126	Akron	0	10	MID	0	0
127	NM St.	1	9	IND	0	0
128	Old Dominion	1	9	USA	0	0
129	S. Alabama	1	9	SUN	0	0
130	UTEP	1	9	USA	0	0