Journal of Statistical Physics

, Volume 125, Issue 4, pp 841–872 | Cite as

Hierarchical Characterization of Complex Networks

  • Luciano da Fontoura CostaEmail author
  • Filipi Nascimento Silva


While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.


complex networks hierarchical measurements disordered systems networks and graphs 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Luciano da Fontoura Costa
    • 1
    Email author
  • Filipi Nascimento Silva
    • 1
  1. 1.Cybernetic Vision Research Group, GII-IFSCUniversidade de São PauloSão CarlosBrasil

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