1 The weighted shortest path arborescence game.

2 A high-efficient algorithm to seek the shortest path arborescence and all shortest paths between any two vertices in DAG is presented.

3 Thus passed the leafy time when arborescence seems to be the one thing aimed at out of doors.

4 The models of shortest path arborescence game and weighted shortest path arborescence game are established and the imputations of this cooperative game in many cases are obtained.

5 With the expansion of information visualization applications, requirement of the control over the length of edges appears in the drawing of weighted arborescence.