A characteristic approach to bipartite graphs as incidence graphs - McKee, Terry A. (Utilitas Mathematica, 2005)
A 'bipartite characteristic' parameter is defined for bipartite graphs that mimics the (Euler) characteristic - the number of. vertices, minus the number of edges, plus the number of triangles, minus the number of 4-cliques, etc. - of general graphs. This allows the characterization of linear, totally balanced, acyclic, tree, and biacyclic hypergraphs in terms of the bipartite characteristic values of their incidence graphs.