Matroidal undirected network

The undirected graphical model is generalized to a linear matroid. The optimal direction for multicasting can be found in polynomial time with respect to the size of the network. A more general problem is also considered where certain function of a distributed source is to be computed at multiple nodes. The converse results are derived, not from the usual cut-set bound but through the related problem of secret key agreement and secure source coding by public discussion. A unifying model of partly directed network can also be formulated, covering both the directed and undirected networks as special cases.