One does not simply walk into an FBS coaching job. The road to such a job is often long and erratic. Coaches usually get jobs by (1) being a great coach at a lower level, or (2) being associated with a great coach by serving on his staff.
Above is an interactive visualization of all of the coaching connections between current FBS head coaches, offensive coordinators, and defensive coordinators. Two coaches are connected if they were on the same staff together at some point during their careers. Coaches on the same staff didn't necessarily have to be head coaches or coordinators when they were together (although some were), but each of them is a head coach or coordinator now.
Describing the Network
Social network analysis gives us many tools we can use to describe our network. I will focus on measures of centrality, which attempt to describe the most "central" coaches along certain metrics. The top coaches for each measure of centrality are in the table below.
| || Betweenness || Eigenvector || Closeness || Degree |
| 1 || Noel Mazzone || Dan McCarney || Charlie Strong || Nick Saban |
| 2 || Kevin Sumlin || Urban Meyer || Urban Meyer || Dan McCarney |
| 3 || Nick Saban || Charlie Strong || Kevin Sumlin || Kevin Sumlin |
| 4 || Art Kaufman || Chuck Heater || Chuck Heater || Charlie Strong |
| 5 || Dan McCarney || Nick Saban || Chris Cosh || Urban Meyer |
| 6 || Mike Locksley || Chris Cosh || Mike Hankwitz || Jim Bollman |
| 7 || Charlie Strong || Dan Mullen || Nick Saban || Mike Locksley |
| 8 || Chris Cosh || Steve Addazio || Dan McCarney || Jimbo Fisher |
| 9 || P. J. Fleck || Vance Bedford || Mike Locksley || Chuck Heater |
| 10 || Matt Wells || Jim Bollman || Brian Polian || Chris Cosh |
Degree centrality measures a number of connections a particular coach has. So, among current FBS HC/coordinators, Nick Saban has the most connections (which is unsurprising), followed by Dan McCarney (see below), Kevin Sumlin, and Charlie Strong.
Closeness centrality measures how far (in terms of tie steps) a particular coach is from every other coach in the graph. Charlie Strong has the lowest average distance between himself and every other coach in the network, followed by Urban Meyer, Kevin Sumlin, Chuck Heater, and Nick Saban.
Betweenness centrality measures how often a coach is a bridge between two other coaches. The coach may bridge two coaches directly, or can merely serve as one point in a much longer bridge. Noel Mazzone, UCLA's offensive coordinator, has the highest betweenness centrality in the graph. He's likely a candidate for a head coaching job in the current 2015 head coaching cycle, or will be next year. Kevin Sumlin, Nick Saban, Art Kaufman, and Dan McCarney round out the top five.
Lastly, eigenvector centrality measures how influential a coach is. Those high in eigenvector centrality have many connections to other influential coaches. Eigenvector centrality is a relative measure, based on the most influential coach. The coach highest in eigenvector centrality is Dan McCarney, current head coach at North Texas. This might sound surprising to some, but Dan McCarney has connections with Urban Meyer (Florida), Charlie Strong (Florida), Steve Addazio (Florida), Bill Snyder (Iowa), Kirk Ferentz (Iowa), and Bob and Mike Stoops (Iowa). This, combined with his high Degree, Betweenness, and Closeness centrality, makes me think he's currently underplaced, and might make a big-ish move soon.
If you want to play around with a bigger version of the network, that's here.