Lecture series »Felix-Klein-Colloquium« / 10. Januar 2017, 17:15 – 18:30 h
Complex Networks as Random Graphs
A network model with preferential attachment is a sequence of random graphs that is formed dynamically according to a simple rule: in each step a new vertex is added and connected to a deterministic or random number of randomly chosen vertices. In this process the new vertex has a preference to form new links with vertices of high degree. As originally pointed out by Barabási and Albert this building mechanism induces heavy tailed degree distributions which is in line with empirical observations.
In this talk we discuss the typical structure of large networks with preferential attachment. In particular we illustrate the artefacts caused by the dynamical building paradigm by comparing the asymptotic results with the ones known for related rank-one networks such as the configuration model.