Closeness is the right metric for the centerpiece question: it rewards being a short hop from everybody, not merely having many teammates. Betweenness measures something different — how often a player is the only reasonable bridge between two others.
Among all chains of the shortest length, the one shown is the strongest: it maximises the games shared on its weakest link, so you never get a chain that hinges on a one-game cameo unless nothing better exists.
Relocations and renames are listed separately, exactly as the source data records them — the Seattle SuperSonics and Oklahoma City Thunder are two entries, not one. Chaining them into single franchise lineages is an editorial call I have deliberately left to you.
Each row uses only the players and connections that existed by that season. A player can gain the crown decades after retiring — the network keeps growing around him, and closeness is relative.