High-degree vertices in Minimum-Component-Distance GIRGs with dimension at least two form expander subgraphs with omega(1) expansion for every sublinear set.
Existence of Small Separators Depends on Geometry for Geometric Inhomogeneous Random Graphs
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abstract
We show that Geometric Inhomogeneous Random Graphs (GIRGs) with power law weights may either have or not have separators of linear size, depending on the underlying geometry. While it was known that for Euclidean geometry it is possible to split the giant component into two linear size components by removing at most n^{1-\eps} edges, we show that this is impossible if the geometry is given by the minimum component distance.
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Expanders in Models of Social Networks
High-degree vertices in Minimum-Component-Distance GIRGs with dimension at least two form expander subgraphs with omega(1) expansion for every sublinear set.