EGBTER: Capturing degree distribution, clustering coefficients, and community structure in a single random graph model

TL;DR

EGBTER is a new random graph model that simultaneously captures degree distribution, clustering coefficients, and community structure, improving upon previous models by offering greater flexibility and accuracy.

Contribution

The paper introduces EGBTER, a novel model that unifies the modeling of degree distribution, clustering, and community structure in a single framework.

Findings

EGBTER accurately models degree distribution, clustering, and communities.

Compared to BTER and GBTER, EGBTER provides better community representation.

Empirical results show EGBTER's superior fit to real-world networks.

Abstract

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.