Eur. Phys. J. B 61, 247-256 (2008)
https://doi.org/10.1140/epjb/e2008-00049-5

Characterization of complex networks by higher order neighborhood properties

¹ Instituto de Física, Universidade Federal da Bahia Campus Universitário da Federação, 40210-340 Salvador, BA, Brazil
² Instituto de Matemática, Universidade Federal da Bahia Campus Universitário da Federação, 40130-240 Salvador, BA, Brazil

Corresponding author: ^a randrade@ufba.br

Received: 20 August 2007
Published online: 6 February 2008

Abstract

A concept of higher order neighborhood in complex networks, introduced previously [Phys. Rev. E 73, 046101 (2006)], is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each higher order neighborhood as a network in itself, represented by a corresponding adjacency matrix, and to settle a plenty of new parameters in order to obtain a best characterization of the whole network. Usual network indices are then used to evaluate the properties of each neighborhood. The identification of high order neighborhoods is also regarded as intermediary step towards the evaluation of global network properties, like the diameter, average shortest path between node, and network fractal dimension. Results for a large number of typical networks are presented and discussed.