Considerable attention has been paid, in recent years, to the use of networks
in modeling complex real-world systems. Among the many dynamical processes
involving networks, propagation processes -- in which final state can be
obtained by studying the underlying network percolation properties -- have
raised formidable interest. In this paper, we present a bond percolation model
of multitype networks with an arbitrary joint degree distribution that allows
heterogeneity in the edge occupation probability. As previously demonstrated,
the multitype approach allows many non-trivial mixing patterns such as
assortativity and clustering between nodes. We derive a number of useful
statistical properties of multitype networks as well as a general phase
transition criterion. We also demonstrate that a number of previous models
based on probability generating functions are special cases of the proposed
formalism. We further show that the multitype approach, by naturally allowing
heterogeneity in the bond occupation probability, overcomes some of the
correlation issues encountered by previous models. We illustrate this point in
the context of contact network epidemiology.Comment: 10 pages, 5 figures. Minor modifications were made in figures 3, 4
and 5 and in the text. Explanations and references were adde