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- W4381245757 abstract "In this paper we study the threshold model of emph{geometric inhomogeneous random graphs} (GIRGs); a generative random graph model that is closely related to emph{hyperbolic random graphs} (HRGs). These models have been observed to capture complex real-world networks well with respect to the structural and algorithmic properties. Following comprehensive studies regarding their emph{connectivity}, i.e., which parts of the graphs are connected, we have a good understanding under which circumstances a emph{giant} component (containing a constant fraction of the graph) emerges. While previous results are rather technical and challenging to work with, the goal of this paper is to provide more accessible proofs. At the same time we significantly improve the previously known probabilistic guarantees, showing that GIRGs contain a giant component with probability $1 - exp(-Omega(n^{(3-tau)/2}))$ for graph size $n$ and a degree distribution with power-law exponent $tau in (2, 3)$. Based on that we additionally derive insights about the connectivity of certain induced subgraphs of GIRGs." @default.
- W4381245757 created "2023-06-20" @default.
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- W4381245757 date "2023-06-15" @default.
- W4381245757 modified "2023-09-26" @default.
- W4381245757 title "On the Giant Component of Geometric Inhomogeneous Random Graphs" @default.
- W4381245757 doi "https://doi.org/10.48550/arxiv.2306.09506" @default.
- W4381245757 hasPublicationYear "2023" @default.
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