This is now a separate post from Graph theory in Formula 1 so that the evolution of the graph of 1-2 finishes can be tracked. The graphs are shown as they were after the race mentioned in the subheading.
Obviously, there is only one edge after the first race of the season, a Mercedes 1-2. This turned out to be the beginning of a series of five 1-2 for Mercedes, so the graph did not change again until Monaco.
At Monaco, Mercedes drivers took “only” the first and third place, as Vettel appeared in top 2.
It began with the youngest ever front row of the F1 grid: Leclerc and Verstappen. And ended with the youngest ever 1-2 finish (represented by an edge here) in Formula One: Verstappen and Leclerc. For the moment, the graph is disconnected.
Two predictions: (1) the components will get connected; (2) the graph will stay with 5 vertices, setting a new record for the fewest number of vertices. Which is a way of saying, I don’t expect either Gasly or anyone outside of top 3 teams to finish in top two for the rest of the season.
The rain-induced chaos in Hockenheim could have added a third component to the graph, but instead it linked the two existing ones. The graph is now a path on 5 vertices, which is not a likely structure in this context.
Sure, the configuration did not last. The graph is longer a tree, and nor longer bipartite.
A prediction added during the summer break: the season’s graph will contain a Hamiltonian cycle.
Getting closer to constructing a Hamiltonian cycle: only one degree-1 vertex remains. The graph is similar to 1992 season, except the appendage was one edge longer then.
In 1992, the central position was occupied by Mansell, who scored 93% more points than the runner-up to the title. This is where we find Hamilton at present, though with “only” 32% more points than the 2nd place. (The percentages are called for, because the scoring system changed in between.)
A Hamiltonian cycle is now complete. The only way to lose it is by adding another vertex to the graph, which I do not expect to happen.
The graph resembles the 2001 season where Hamilton’s position was occupied by Schumacher. The only difference is that in 2001, there was an extra edge incident to Schumacher.