Tuning degree distributions: Departing from scale-free networks

2006/02/28 by Christopher Leary, C. C. Leary, M. Schwehm +5
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Cartography #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Degree (music) #Degree distribution #Gene Regulatory Network Analysis #Geography #Mathematics #Opinion Dynamics and Social Influence #Physics #Scale (ratio) #Scale-free network #Statistical physics #physics.data-an

paper · pdf · doi:10.1016/j.physa.2007.04.058

13 pages, 5 figures. Submitted to Physical Review E; references added, intro rewritten

arxiv created 2006/04/05 · openalex publication_date 2007/04/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed networks, however, often differ from the power-law type and data based investigations require modifications of the typical scale-free network. We present an algorithm that generates networks in which the skewness of the degree distribution is tuneable by modifying the preferential attachment step of the Barabasi-Albert construction algorithm. Skewness is linearly correlated with the maximal degree of the network and, therefore, adequately represents the influence of superspreaders or hubs. By combining our algorithm with work of Holme and Kim, we show how to generate networks with skewness gamma and clustering coefficient kappa, over a wide range of values.

Citations

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