A spatially weighted degree model for network vulnerability analysis

Using degree distribution to assess network vulnerability represents a promising direction of network analysis. However, the traditional degree distribution model is inadequate for analyzing the vulnerability of spatial networks because it does not take into consideration the geographical aspects of spatial networks. This paper proposes a spatially weighted degree model in which both the functional class and the length of network links are considered to be important factors for determining the node degrees of spatial networks. A weight coefficient is used in this new model to account for the contribution of each factor to the node degree. The proposed model is compared with the traditional degree model and an accessibility-based vulnerability model in the vulnerability analysis of a highway network. Experiment results indicate that, although node degrees of spatial networks derived from the traditional degree model follow a random distribution, node degrees determined by the spatially weighted model exhibit a scale-free distribution, which is a common characteristic of robust networks. Compared to the accessibility-based model, the proposed model has similar performance in identifying critical nodes but with higher computational efficiency and better ability to reveal the overall vulnerability of a spatial network.