Shortest paths and load scaling in scale-free trees

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© 2002 American Physical Society (APS). This is the accepted version of the following article: Szabó, Gábor & Alava, Mikko J. & Kertész, János. 2002. Shortest paths and load scaling in scale-free trees. Physical Review E. Volume 66, Issue 2. 026101/1-8. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.66.026101, which has been published in final form at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.66.026101.

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Journal Title

Journal ISSN

Volume Title

School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2002

Major/Subject

Mcode

Degree programme

Language

en

Pages

026101/1-8

Series

Physical Review E, Volume 66, Issue 2

Abstract

The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabási-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a Gaussian in the limit of N large. The load, the number of the shortest distance paths passing through any node, is discussed in the tree presentation.

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Keywords

scale-free trees, Barabási-Albert model

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Citation

Szabó, Gábor & Alava, Mikko J. & Kertész, János. 2002. Shortest paths and load scaling in scale-free trees. Physical Review E. Volume 66, Issue 2. 026101/1-8. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.66.026101.