A bidirected generalization of network matrices

We define binet matrices, which furnish a direct generalization of totally unimodular network matrices and arise from the node-edge incidence matrices of bidirected graphs in the same way as the network matrices do from directed graphs. We develop the necessary theory, give binet representations for interesting sets of matrices, characterize totally unimodular binet matrices and discuss the recognition problem. We also prove that binet matrices guarantee half-integral optimal solutions to linear programs.