Iterative models for complex networks formed by extending cliques

TL;DR

This paper introduces the frustum model for complex networks, which extends dense subgraphs iteratively, resulting in graphs that densify over time and exhibit properties like small-world behavior, with potential applications in understanding real-world networks.

Contribution

The paper proposes a novel iterative model for complex networks based on extending cliques, demonstrating properties like densification and small-world characteristics in generated graphs.

Findings

Graphs densify over time under certain parameters

Generated graphs exhibit small-world properties

Models open new avenues for studying real-world networks

Abstract

We consider a new model for complex networks whose underlying mechanism is extending dense subgraphs. In the frustum model, we iteratively extend cliques over discrete-time steps. For many choices of the underlying parameters, graphs generated by the model densify over time. In the special case of the cone model, generated graphs provably satisfy properties observed in real-world complex networks such as the small world property and bad spectral expansion. We finish with a set of open problems and next steps for the frustum model.