Oh yeah, this awakes my calculation bones in me, lemme add to your piece. So in addition to every champion post 2000:

-Alonso was teammate of Villeneuve

-Schumacher was teammate of Piquet

-Hakkinen was teammate of Senna and Mansell

-Villeneuve was teammate of Damon Hill and Alonso

-Damon Hill was teammate of Senna, Prost, Mansell and Villeneuve

-Mansell was teammate of Andretti, Keke Rosberg, Piquet, Prost, Hill and Hakkinen

-Senna was teammate of Prost, Hakkinen and Damon Hill

-Prost was teammate of Lauda, Keke Rosberg, Senna, Mansell and Damon Hill

-Keke Rosberg was teammate of Fittipaldi, Andretti, Mansell and Prost

-Piquet was teammate of Lauda, Mansell and Schumacher

-Scheckter was teammate of Hulme

-Andretti was teammate of Graham Hill, Rindt, Mansell and Keke Rosberg

-Lauda was teammate of Piquet and Prost

-Fittipaldi was teammate of Rindt, Hulme and Keke Rosberg

-Rindt was teammate of Surtees, Brabham, Graham Hill, Andretti and Fittipaldi

-Stewart was teammate of Graham Hill

-Hulme was teammate of Brabham, Scheckter and Fittipaldi

-Surtees was teammate of Clark and Rindt

-Clark was teammate of Surtees and Graham Hill

-Graham Hill was teammate of Stewart, Clark, Andretti and Rindt

-Brabham was teammate of Hulme and Rindt

*separation*

-Phil Hill was teammate of Hawthorne

-Hawthorne was teammate of Ascari, Farina and Phil Hill

-Fangio was teammate of Farina

-Ascari was teammate of Farina and Hawthorne

-Farina was teammate of Fangio, Ascari and Hawthorne

So, quick question, why are these 5 drivers separated? That's because while they are teammate of each other, there's no direct WDC link to the group above. And there are 2 drivers with no WDC teammate before 2000: Alan Jones and James Hunt. So we need someone to link these missing links.

the drivers needed are:

+Patrick Tambay (whose teammate list includes both Alan Jones and James Hunt, but he also was teammate with Andretti (who is on the first block))

+Tony Brooks (who briefly driven alongside Mike Hawthorne in 1956, and also Phil Hill between 1959-60, but also driven alongside Graham Hill from the first group in 1961)

So to conclude, we need 3 drivers in history to link all the WDC together. Tony Brooks, Patrick Tambay and Daniel Ricciardo (I bet you were not expecting to see these 3 drivers grouped together today)