# American Institute of Mathematical Sciences

June  2008, 3(2): 277-294. doi: 10.3934/nhm.2008.3.277

## Augmenting $k$-core generation with preferential attachment

 1 Faculty of Informatics, Universität Karlsruhe (TH), 78131 Karlsruhe, Germany, Germany, Germany, Germany, Germany

Received  August 2007 Revised  March 2008 Published  March 2008

The modeling of realistic networks is of prime importance for modern complex systems research. Previous procedures typically model the natural growth of networks by means of iteratively adding nodes, geometric positioning information, a definition of link connectivity based on the preference for nearest neighbors or already highly connected nodes, or combine several of these approaches.
Our novel model brings together the well-know concepts of $k$-cores, originally introduced in social network analysis, and of preferential attachment. Recent studies exposed the significant $k$-core structure of several real world systems, e.g., the AS network of the Internet. We present a simple and efficient method for generating networks which at the same time strictly adhere to the characteristics of a given $k$-core structure, called core fingerprint, and feature a power-law degree distribution. We showcase our algorithm in a com- parative evaluation with two well-known AS network generators.
Citation: Michael Baur, Marco Gaertler, Robert Görke, Marcus Krug, Dorothea Wagner. Augmenting $k$-core generation with preferential attachment. Networks & Heterogeneous Media, 2008, 3 (2) : 277-294. doi: 10.3934/nhm.2008.3.277
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