Universal scaling of distances in complex networks

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equal...

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Bibliographic Details
Published in:arXiv.org 2005-09
Main Authors: Holyst, Janusz A, Sienkiewicz, Julian, Fronczak, Agata, Fronczak, Piotr, Suchecki, Krzysztof
Format: Article
Language:English
Subjects:
Apexes
Clustering
Public transportation
Scaling
Transportation networks
Online Access:Get full text
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Summary:Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equals to =A-B log(k_i k_j). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree _nn calculated for the nearest neighbors and on network clustering coefficients.
ISSN:2331-8422
DOI:10.48550/arxiv.0411160