The largest subcritical component in inhomogeneous random graphs of preferential attachment type
Abstract
Abstract We identify the size of the largest connected component in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The component is polynomial in the graph size with an explicitly given exponent, which is strictly larger than the exponent for the largest degree in the graph. This is in stark contrast to the behaviour of inhomogeneous random graphs with a kernel of rank one. Our proof uses local approximation by branching random walks going well beyond the weak local limit and novel results on subcritical killed branching random walks.
Fields of Study & Subjects
Graph theory and applications
Complex Network Analysis Techniques
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Combinatorics Probability Computing
- Publisher
- Cambridge University Press (CUP)
- Volume
- 35
- Issue
- 3
- Pages
- 414–432
- Publication date
- 4 March 2026
- Language
- EN