Disorder and decision cost in spatial networks

Zanin, Massimiliano; Buldú, Javier M.; Cano Vila, Pedro; Boccaletti, Stefano

doi:http://dx.doi.org/10.1063/1.2901916

Disorder and decision cost in spatial networks

Citation

Zanin M, Buldú JM, Cano P, Boccaletti S. Disorder and decision cost in spatial networks. Chaos. 2008;18(2):023103 DOI: 10.1063/1.2901916

Abstract

We introduce the concept of decision cost of a spatial graph, which measures the disorder of a given network taking into account not only the connections between nodes but their position in a two-dimensional map. The influence of the network size is evaluated and we show that normalization of the decision cost allows us to compare the degree of disorder of networks of different sizes. Under this framework, we measure the disorder of the connections between airports of two different countries and obtain some conclusions about which of them is more disordered. The introduced concepts (decision cost and disorder of spatial networks) can easily be extended to Euclidean networks of higher dimensions, and also to networks whose nodes have a certain fitness property (i.e., one-dimensional). When analyzing structures tailored by men, complex networks theory has been a useful instrument in order to study their complexity. In many works related to this field, the projected network is obtained by detecting connections between their fundamental units (i.e., nodes), disregarding any information about their spatial distribution. In this paper, we study the importance of the Euclidean position of nodes for a key property of the network: the decision cost, that is, the difficulty for a blind agent to make its way from a starting node to a target node. We demonstrate how this parameter is a good indicator of the disorder of a spatial net, and we apply this measure to two different airport networks.