Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, November 12, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Ralph Keusch

Small-world phenomena on Geometric Inhomogeneous Random Graphs

Recently, with Geometric Inhomogeneous Random Graphs (GIRGs) we introduced a new model for the theoretical study of real-world networks. Typically, such networks exhibit so-called small-worlds: the average distance between two random vertices is very small, although the networks are sparse. In this talk, we show that GIRGs have good connectivity properties: we prove the existence of a giant component of linear size, polylogarithmic diameter and ultra-small average distance of order only log(log(n)) within the giant.
This is joint work with Karl Bringmann and Johannes Lengler. The talk is subsequent to Johannes' presentation on Tuesday where we have seen an overview of the model, the variants and the different results, but can be attended independently.

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