The ordinal potential game has a large number of applications. It is proved that a finite game is ordinal potential game if and only if its potential directed graph(PDG) contains no unidirectional circle. The adjacency matrix of PDG is obtained by the payoff matrix. By Reducing connected bidirectional circles into a node, the problem of judging the existence of unidirectional circles is converted, into testifying the existence of cycles in the reduced graph. Furthermore, some properties of ordinal potential function(OPF) and its calculating method are presented. Finally, combined with linear programming, the application of ordinal potential game in prolonging the lifetime of agent wireless networks is studied.