In most domains of network analysis researchers consider networks that arise
in nature with weighted edges. Such networks are routinely dichotomized in the
interest of using available methods for statistical inference with networks.
The generalized exponential random graph model (GERGM) is a recently proposed
method used to simulate and model the edges of a weighted graph. The GERGM
specifies a joint distribution for an exponential family of graphs with
continuous-valued edge weights. However, current estimation algorithms for the
GERGM only allow inference on a restricted family of model specifications. To
address this issue, we develop a Metropolis--Hastings method that can be used
to estimate any GERGM specification, thereby significantly extending the family
of weighted graphs that can be modeled with the GERGM. We show that new
flexible model specifications are capable of avoiding likelihood degeneracy and
efficiently capturing network structure in applications where such models were
not previously available. We demonstrate the utility of this new class of
GERGMs through application to two real network data sets, and we further assess
the effectiveness of our proposed methodology by simulating non-degenerate
model specifications from the well-studied two-stars model. A working R version
of the GERGM code is available in the supplement and will be incorporated in
the gergm CRAN package.Comment: 33 pages, 6 figures. To appear in Social Network