Bipartite graphs are TUM.
Directed graphs are TUM.
Max-flow min-cut theorem is a restatement of TUMity
Network matrices (NM) are TUM. NM
Look up these lecture notes on network matrices. The complete lecture notes is this. The lecture notes give the significant points about TUMity. Also the thesis by Koyntek, which introduces "binet matrices", a generalization of NM. There are some good explanations (esp. figures) in the thesis that are not present in either Schrijver's book or in the book by Cook et. al.
M seems to mean a flow. Is that right?