## Abstract

We report on the exact results for the degree K, the diameter D, the clustering coefficient C, and the betweenness centrality B of a hierarchical network model with a replication factor M. Such quantities are calculated exactly with the help of recursion relations. Using the results, we show that (i) the degree distribution follows a power law [Formula presented] with [Formula presented] (ii) the diameter grows logarithmically as [Formula presented] with the number of nodes N, (iii) the clustering coefficient of each node is inversely proportional to its degree, [Formula presented] and the average clustering coefficient is nonzero in the infinite N limit, and (iv) the betweenness centrality distribution follows a power law [Formula presented] We discuss a classification scheme of scale-free networks into the universality class with the clustering property and the betweenness centrality distribution.

Original language | English |
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Pages (from-to) | 4 |

Number of pages | 1 |

Journal | Physical Review E |

Volume | 67 |

Issue number | 4 |

DOIs | |

State | Published - 2003 |