### 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.

Original language | English |
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Article number | 026101 |

Pages (from-to) | 1-8 |

Journal | Physical Review E |

Volume | 66 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 |

MoE publication type | A1 Journal article-refereed |

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## Cite this

Szabo, G., Alava, M., & Kertesz, J. (2002). Shortest paths and load scaling in scale-free trees.

*Physical Review E*,*66*(2), 1-8. [026101]. https://doi.org/10.1103/PhysRevE.66.026101