Navigational evaluation of breadth first search spanning trees

Decentralized navigation is one of the most important functions of complex networks. A wide variety of different networks such as communication, social, or information networks possesses certain structural clues which allow navigational agents to efficiently navigate those networks even with local knowledge of the network only. Such structural clues include node degrees and their centralities, similarities between nodes, or node clustering coefficients. In practice, those properties may be combined and abstracted in the form of a distance metric on the network node set - a typical representation of such a distance metric is a hierarchy of network nodes where the most central nodes are situated in the upper levels of the hierarchy and the hierarchy links capture the node similarities or their clustering. Recently, a number of algorithms for extracting such hierarchies have been introduced. The majority of those algorithms is based on complex and computationally intensive methods such as hierarchical clustering. In this paper we analyze several simple spanning tree algorithms and their ability to extract sound hierarchies for network navigation. In particular, we are interested in correlation of structural node properties (such as node degree) and the navigational quality of spanning trees that are rooted at those nodes. Our work sheds light on the ability of spanning trees to serve as a distance metric for decentralized navigation in networks. Our results are relevant for scientists interested in the navigability of complex networks and for engineers who are interested in fast and simple extraction of hierarchies for supporting navigation in networks.