Abigail Raz, Cooper Union
Authors: Abigail Raz and Erin Meger
2023 AWM Research Symposium
Extremal and Probabilistic Combinatorics [Organized by Jinyoung Park and Corrine Yap]

Deterministic complex networks that use iterative generation algorithms have been found to more closely mirror properties found in real world networks than the standard uniform random graph models. In this talk I will introduce a new, Iterative Independent Model (IIM), significantly generalizing previously studied models. These models use ideas from Structural Balance Theory to generate edges through a notion of cloning where ``the friend of my friend is my friend'' and anticloning where ``the enemy of my enemy is my friend.'' We found that all graphs generated in this manner have common properties such as a spectral gap (of the normalized Laplacian) bounded away from 0 and low diameter and domination number. Additionally, for any fixed graph F all IIM graphs will eventually contain an induced copy of F. We may also discuss zero forcing on such graphs. Together this indicates that IIM graphs share more properties, and thus better mimic, social networks then traditional uniformly randomly generated graphs.

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