  We consider a directed acyclic network with multiple sources and multiple
terminals where each terminal is interested in decoding the sum of independent
sources generated at the source nodes. We describe a procedure whereby a simple
undirected graph can be used to construct such a sum-network and demonstrate an
upper bound on its computation rate. Furthermore, we show sufficient conditions
for the construction of a linear network code that achieves this upper bound.
Our procedure allows us to construct sum-networks that have any arbitrary
computation rate $\frac{p}{q}$ (where $p,q$ are non-negative integers). Our
work significantly generalizes a previous approach for constructing
sum-networks with arbitrary capacities. Specifically, we answer an open
question in prior work by demonstrating sum-networks with significantly fewer
number of sources and terminals.
