  A concept of higher order neighborhood in complex networks, introduced
previously (PRE \textbf{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. Usual network indices are then used to
evaluate the properties of each neighborhood. Results for a large number of
typical networks are presented and discussed. Further, the information from all
neighborhoods is condensed in a single neighborhood matrix, which can be
explored for visualizing the neighborhood structure. On the basis of such
representation, a distance is introduced to compare, in a quantitative way, how
far apart networks are in the space of neighborhood matrices. The distance
depends both on the network topology and the adopted node numbering. Given a
pair of networks, a Monte Carlo algorithm is developed to find the best
numbering for one of them, holding fixed the numbering of the second network,
obtaining a projection of the first one onto the pattern of the other. The
minimal value found for the distance reflects differences in the neighborhood
structures of the two networks that arise from distinct topologies. Examples
are worked out allowing for a quantitative comparison for distances among a set
of distinct networks.
