After some games it seems that the Ancient Chinese Weiqi game does expose additional implicit information about the board. Give any vertex and edge it is clear the axis on which it lie and the direction from the vertex it emanates: e.g. north of the vertex. This information is lost when we represented the game as a graph.
Therefore the information is injected by using directed graph and labeled edges. Therefore, let the board be
- Set of players P, typically players are distinguished by color. E.g. black and white.
- Set of verteces V.
- Set of directed edges between them: V X V.
- Disjoint sets of edges known as axis representing edges that lie in the direction of that axis: eg the north-south axes is one set, east-west a separate and disjoint set, up-down a third set.
- Liberty can only flow in the direction of edge. A stone s receive 1 liberty from an unoccupied vertex c if (v,s) is an edge. A stone s may benefit from all liberties of a second stone t if (t,s) is an edge.