Largest subcritical component in preferential attachment model variants

Determine the size of the largest subcritical connected component for preferential attachment network models beyond the simplified inhomogeneous random graph of preferential attachment type studied here.

Background

The paper notes that the order of the largest subcritical component had been established for the configuration model but not for preferential attachment models generally. The present work resolves the problem for a simplified inhomogeneous random graph whose kernel is chosen to reproduce key preferential-attachment features, while leaving the corresponding question for other preferential attachment model variants unresolved.

References

In particular, the problem of the size of the largest subcritical connected component, solved for the configuration model by Janson, is open for all model variants of preferential attachment.

— The largest subcritical component in inhomogeneous random graphs of preferential attachment type  (2503.05469 - Mörters et al., 7 Mar 2025) in Section 1, Introduction and main results