 formula_2 is central if the subgraph of formula_1 formed by removing all the vertices of formula_2 has a perfect matching; central cycles are also sometimes called alternating circuits.And formula_2 is oddly oriented if each of the two orientations of formula_2 is consistent with an odd number of edges in the orientation.Pfaffian orientations have been studied in connection with the FKT algorithm for counting the number of perfect matchings in a given graph.