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The local weak limit of GIRGs
Let $\mathrm{GIRG}_{W,L}(n)$ denote the finite geometric inhomogeneous random graph with weight distribution $W$ and edge-length distribution $L$ , and suppose it satisfies the exte…
Conjectureopengeometric-inhomogeneous-random-graphs local-weak-convergence random-graphsarXiv posted 2 days ago
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Existence of a giant component in finite-variance GIRGs
A GIRG is a geometric inhomogeneous random graph with power-law weight exponent $\tau$ and an edge-density parameter. In the finite-variance regime, $\tau>3$ , and when the edge-den…
Conjectureopengeometric-inhomogeneous-random-graphs giant-components random-graphsarXiv posted 2 days ago
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Conjecture on bounded average distances in GIRGs
Consider a geometric inhomogeneous random graph (GIRG) on a box of volume $n$ , with vertex weights following a power-law distribution of exponent $\widetilde\tau\in(2,3)$ . Add i.i.…
Conjectureopenfirst-passage-percolation geometric-inhomogeneous-random-graphs scale-free-percolationarXiv posted 2 days ago

The local weak limit of GIRGs