The Study Of Spatial Weighted Network Model And Strength-degree Correlation

The study of the complex network model takes the phenomenological method to investigate the internal mechanism of the self-organized network evolvement.The models are proposed to reproduce all kinds of statistical properties found in the real-world network so that they can provide some meaningful insights to the evolvement and the nontrivial properties that the networks exhibit.Recent years some weighted network models and spatial network models have been proposed and they are able to reproduce some properties of the real-world network. However there are still many problems that need to be explored:1.For spatial network, the cost to construct the network is generally considered to be the basic mechanism that affects the formation of the network.But the construction of the real-world network depends not only on the cost hut also on the prediction of the expected benefit.Studies from this perspective are still untouched.2.As to the issue of strength-degree correlation, despite that some models can reproduce the linear and nonlinear correlation,none of them reveals the underlying cause that should be responsible for the two different strength-degree correlation.3.The models coupling simultaneously with the topology, weight and spatial consideration are not sufficiently studied.Motivated by the three points,we proposed a gravity model for spatial weighted network by introducing the concept of expected traffic and discussed detailedly the issue of the strength-degree correlation.The contribution of the paper is shown as follow:1.The gravity model:The expected traffic is introduced and can be measured by the gravity equation.Then a spatial weighted network model is proposed based on the optimal expected traffic.The model can change its topology by varying two parametersαandγand the airline-like or internet-like topology can emerge respectively during the transition.The statistical properties of the model studied in detail including the degree distribution,clustering-degree distribution,degree correlation,hierarchical organization and edge length distribution,etc.A simulation for real Chinese city airline network is completed.2.The transport effect is responsible for the nonlinear strength-degree correlation: The analytical correlation of strength and degree is derived from the concept of the expected traffic.And the linear and nonlinear strength-degree correlation can emerge when considering and neglecting the "transport effect",respectively.Thus the emergence of the linear and nonlinear strength-degree correlation are possible to be explained under a common framework which is very intuitionistic to account for the reason why the strength-degree correlation behaves different for social network and technical network.This result is applied to the Chinese city airline network and the correlation exponent is found to be coincident with the real data.Finally we discuss the mechanism of the network evolvement.