Here is a corrected version of the slides for my talk at the Probl@b Seminar in Bath on 19 March. The talk also included some material about recent work on scale free preferential attachment networks with “critical” power law exponent .
I am going to speak about random networks (in particular about doubly logarithmic distances in power law random graphs) at the German Probability and Stochastic Days in Mainz (06/03 – 09/03 2012) in the section about random discrete structures and analysis of algorithms. Here are the presentation slides.
Here are some links to (old) presentations I gave about distances in random network. In March 2010 I spoke in the Problab Seminar Series in Bath, the slides provide some introductory material about Random Networks. In October 2011, I contributed a talk to the Summer School of the BMS on Random Graphs and Random Motions, entitled “Typical Distances in Ultrasmall Random Networks“.
Posted in Talk, Workshop
This is joint work with my PhD supervisor Peter Mörters and Steffen Dereich. We show that in preferential attachment models with power-law exponent the distance between
randomly chosen vertices in the giant component is asymptotically equal to
, where denotes the number of nodes. This is
twice the value obtained for the configuration model with the same
power-law exponent. The extra factor reveals the different structure of typical
shortest paths in preferential attachment graphs.
UPDATE: The article has appeared in Advances in Applied Probability.