  Random graph models are important constructs for data analytic applications
as well as pure mathematical developments, as they provide capabilities for
network synthesis and principled analysis. Several models have been developed
with the aim of faithfully preserving important graph metrics and
substructures. With the goal of capturing degree distribution, clustering
coefficient, and communities in a single random graph model, we propose a new
model to address shortcomings in a progression of network modeling
capabilities. The Block Two-Level Erd{\H{o}}s-R{\'e}nyi (BTER) model of
Seshadhri et al., designed to allow prescription of expected degree and
clustering coefficient distributions, neglects community modeling, while the
Generalized BTER (GBTER) model of Bridges et al., designed to add community
modeling capabilities to BTER, struggles to faithfully represent all three
characteristics simultaneously. In this work, we fit BTER and two GBTER
configurations to several real-world networks and compare the results with that
of our new model, the Extended GBTER (EGBTER) model. Our results support that
EBGTER adds a community-modeling flexibility to BTER, while retaining a
satisfactory level of accuracy in terms of degree and clustering coefficient.
Our insights and empirical testing of previous models as well as the new model
are novel contributions to the literature.
