  In this paper we present a generalization of the classical configuration
model. Like the classical configuration model, the generalized configuration
model allows users to specify an arbitrary degree distribution. In our
generalized configuration model, we partition the stubs in the configuration
model into b blocks of equal sizes and choose a permutation function h for
these blocks. In each block, we randomly designate a number proportional to q
of stubs as type 1 stubs, where q is a parameter in the range [0; 1]. Other
stubs are designated as type 2 stubs. To construct a network, randomly select
an unconnected stub. Suppose that this stub is in block i. If it is a type 1
stub, connect this stub to a randomly selected unconnected type 1 stub in block
h(i). If it is a type 2 stub, connect it to a randomly selected unconnected
type 2 stub. We repeat this process until all stubs are connected. Under an
assumption, we derive a closed form for the joint degree distribution of two
random neighboring vertices in the constructed graph. Based on this joint
degree distribution, we show that the Pearson degree correlation function is
linear in q for any fixed b. By properly choosing h, we show that our
construction algorithm can create assortative networks as well as
disassortative networks. We present a percolation analysis of this model. We
verify our results by extensive computer simulations.
