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

10.20347/WIAS.PREPRINT.3011

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).

Appeared in

  • M. Dewar, P. Prałat, P. Szufel, F. Théberge, M. Wrzosek, eds., vol. 13894 of Lecture Notes in Computer Science, Springer, Cham, 2023, pp. 19--35, DOI 10.1007/978-3-031-32296-9_2 .

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