## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, April 29, 2010, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Ueli Peter

## Non-growing preferential attachment random graphs

Random graph processes are widely used to model the evolution of complex weblike networks. We consider the following simple process that has been proposed to model the dynamics of non-growing networks.

Input: a multigraph on $n$ vertices and $m$ edges and a preference function $f$.

Repeat the following steps:
1. Choose an edge $(v_i, v_j)$ uniformly at random.
2. Select a vertex $v_l$ at random proportional to f(deg(v_l)).
3. Rewire $(v_i, v_j)$ to $(v_i, v_l)$.

We show that the process converges in $O(m\log m)$ steps and present a framework that simplifies the calculation of graph properties in its stationary distribution.

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