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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Lorenzo Federico
Luiss Guido Carli
Electrical & Electronics Engineering

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Connectivity of Poissonian inhomogeneous random multigraphs Lorenzo Federico
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.1.8

Abstract

We introduce a model for inhomogeneous random graphs designed to have a lot of flexibility in the assignment of the degree sequence and the individual edge probabilities while remaining tractable. To achieve this we run a Poisson point process over the square [0, 1]2, with an intensity proportional to a kernel W(x, y) and identify every couple of vertices of the graph with a subset of the square, adding an edge between them if there is a point in such subset. This ensures unconditional independence among edges and makes many statements much easier to prove in this setting than in other similar models. Here we prove sharpness of the connectivity threshold under mild integrability conditions on W(x, y).
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