Modeling And Analysis On Robustness Evaluation Of Spatial Network

Spatial network is a normal topological network embedded in euclidean plane,which is more complicated than its topological network.Different from topological network,research of spatial network starts relatively late,and spatial network robustness has been attached importance since the beginning of the 21 st century.Infrastructure network is one kind of specific networks which heavily rely on physical infrastructure,making itself vulnerable to physical multiple damages,such as physical multiple attacks,as well as natural disasters.No matter disasters or attacks affect a specific geographical area and result in failures of neighboring components.Because infrastructure networks are crucial for our everyday living and the national safety,research on the robustness and vulnerability of spatial networks to damages is very important.However,there are not many methods available.To solve this problem,we focus on the components failure caused by located geographical attacks on the network.We present the definition and many characters of spatial network,and present the geometric graph model and the weighted model of spatial network.In particular,the circle cut is assumed as disasters or attacks' damage area.We present two evaluation models to analyse the spatial network.The first model is the robustness evaluation model of spatial network based on critical radius.Two damage models are presented in the model: One is Barycenter-Method(BCM),which calculates the barycenter of the weighted spatial network as damage center,and figures out the critical radius which makes network collapse.The other one is Average random center Method(ARCM),which chooses the damage center among the spatial network randomly and figures out the critical radius,and repeats the algorithm 100 times to get the average result.The second model is the robustness evaluation model of spatial network based on multiple damages.Also two models are presented:One is Multiple Barycenter Attacks Model(MBM),which calculates the positions of damage centers by the given radius based on the barycenters of node pairs and figures out the amount of damages which make network collapse.The other one is Multiple Average Random Attacks Model(MARM),which constantly and randomly chooses the damage centers among the spatial network to make network collapse,and repeats the algorithm 100 times to get the average result.We present the actual data of Chilean electric power grids distribution network(CPN)and American fiber distribution network(AFN)as numerical data.We present many methods,especially the visual method to analyse the numerical results,and the numerical results demonstrate the feasibility of the two evaluation models.This paper is the first attempt to evaluate the robustness of spatial networks.Most kinds of spatial networks' robustness,especially infrastructure networks,can be evaluated by the two models presented in this paper.