Serious Fun
In my last few essays I've analyzed the schedule graph using various tools. From a rating system perspective, though, we're more interested in the games graph. Instead of a↔b meaning "a plays b" rating systems depend upon "a played b" and the games graph changes with every completed game.
Date  #Games  CI%  APL  #Paths  Paths/Pair  #Paths/Game  Diameter  #Pairs at D 
23Sep  138  4.75  8.22  12258  1.70  88.83  19  3 
30Sep  189  8.47  4.67  15828  2.19  83.75  9  1 
7Oct  239  13.17  3.74  18279  2.53  76.48  7  1 
14Oct  290  18.49  3.28  22600  3.12  77.93  5  394 
21Oct  343  23.67  3.05  26266  3.63  76.58  5  91 
28Oct  399  28.74  2.88  29286  4.05  73.40  5  15 
4Nov  453  33.04  2.75  31251  4.31  68.99  5  1 
11Nov  506  36.39  2.66  31997  4.41  63.24  4  712 
18Nov  563  39.85  2.58  31316  4.31  55.62  4  478 
25Nov  614  42.58  2.54  31524  4.33  51.34  4  350 
2Dec  662  45.49  2.49  31543  4.33  47.65  4  255 
9Dec  674  46.23  2.48  31441  4.31  46.65  4  238 
16Dec  675  46.30  2.48  31549  4.32  46.74  4  237 

 Date
 is the last day of the "college football week" running ThursdayWednesday; 23Sep includes the first three weekends
 Games
 is the number of games scheduled to be played through Date
 CI%
 is the percentage of all 7140 teampairs that are connected by paths of length one or two (they have either played each other or at least one common opponent.)
 APL
 is the Average Path Length between two teams
 #Paths
 is the number of unique paths that are the shortest between any pair of teams
 Paths/Pair
 is the average number of unique paths that connect any two teams
 #Paths/Game
 is the average number of unique paths games contribute to
 Diameter
 is the length of the longest path required to connect two teams
 #Pairs at D
 is the number of teampairs for which "diameter"length paths are required to connect the teams
There are "milestones" that have to be achieved for various categories of rating systems to provide meaningful results, and the serious part of this analysis has to do with finding those for the different categories. To begin, note that there are 7140 teampairs x⇔y in the FBS. Here I use ⇔ to mean the shortest connecting paths
↔a_{1}↔a_{2}↔...a_{λ1}↔ where λ is distance(x,y). Also note that except for headtohead (x↔y) there are more than one of these for each pair.
Advanced rating systems depend upon these connecting paths to form their ratings. After week 3 the average game's results are used to compare nearly 88 other pairs of teams  varying from 436 other pairs being ranked based upon the results of Army vs Eastern Michigan down to 6 games whose results can be used only to relate the pair represented by each team's single other opponent. In general, the fewer teams whose relative ratings depend upon a single game's outcome, the more "connected" the field and accurate an advanced system's results:
On the other hand, the more unique paths that connect each pair, the more data the advanced systems have to work with and again, the more accurate their results:
Milestones
The table above begins after weekend three because until the field is connected almost no advanced rating can produce results based only upon this year's results. After the second weekend there are still four teams who've played no games against an FBS opponent (one FCS game and an off week.)
An interesting side note is that weekend three is the earliest the field has become connected since I began making these measurements. Despite the profusion of games vs FCS opponents, there's more interregional FBS games than in prior years.
In week 8 (games through October 28^{th}):
 more than a quarter of all teampairs are related by no worse than an Opponent's opponent relationship
 the average path length becomes ≤ 3
and
 the average number of unique paths per pair becomes ≥ 4
Different ratings may depend upon different features of the games graph, and at least some consider one or more of these significant. Last year, Jeff Sagarin's ratings became "unbiased" (by prior year results) when the games graph connected 25% of the field by no worse than an OO relationship. This doesn't imply that's the criterion Jeff uses, but even if a coincidence this date is a "milestone."
In week 10 (games through November 11^{th}):
 the diameter of the games graph becomes as small as it will ever be
 the average number of paths connecting teampairs is as large as it will ever be
It is at this point that scheduled games make the games graph "denser" by shortening x⇔y paths without creating new paths  sameconference x⇔y's become x↔y eliminating all the λ= 4 paths between x and y but adding shorter paths for their opponents who play one of but not both x and y (o_{x}↔x↔y↔o_{y}). After week 10 most advanced ratings are "stable", and more games just make their rating more precise.