Entanglement (graph measure)
The entanglement game is played by "n" cops against a robber on
a directed graph "G". Initially, all cops are outside the graph and the robber selects an arbitrary starting vertex
"v" of "G". Further on, the players move in turn. In each move the cops either stay where they are, or place one
of them on the vertex currently occupied by the robber. The robber must move from her current vertex, along an edge,
to a successor that is not occupied by a cop. The robber must move if no cop is following him. If there is
no free successor to which the robber can move, she is caught, and the cops win. The robber wins if she
cannot be caught, i.e. if the play can be made to last forever. A graph "G" has entanglement "n" if "n" cops win in the entanglement game on "G" but "n" − 1 cops lose the game. Graphs of entanglement zero and one can be characterized as follows:

Entanglement has also been a key notion in proving that the variable hierarchy
of the modal mu calculus is strict.
Definition
It is defined in terms of a mathematical game in which
"n" cops try to capture a robber, who escapes along the edges of the graph.