WIAS Preprint No. 3011, (2023)
The emergence of a giant component in one-dimensional inhomogeneous networks with long-range effects
Authors
- Gracar, Peter
- Lüchtrath, Lukas
ORCID: 0000-0003-4969-806X - Mönch, Christian
2020 Mathematics Subject Classification
- 05C80
Keywords
- Long-range effects, percolation, phase transition, spatial random graphs, preferential attachment, Boolean model
DOI
Abstract
We study the weight-dependent random connection model, a class of sparse graphs featuring many real-world properties such as heavy-tailed degree distributions and clustering. We introduce a coefficient, (deltaf), measuring the effect of the degree-distribution on the occurrence of long edges. We identify a sharp phase transition in (deltaf) for the existence of a giant component in dimension (d=1).
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