The Study Of Topology Structure And Transport Properties On Complex Gradient Networks

Recently, scientists have showed great interests in studying complex systems from the perspective of complex networks. The main research in this area includes the static structure and the evolution dynamics of the network, the relation between the function and network structure, the practical application of network theory etc, of which the relation between the function and network structure is the key to researching complex networks. Different network achieves different features, transport function is very important of many complex networks. Not only is the transport properties of the network related to the network structure, but also it is related to the route rule which is chosen. Transport processes are often caused by local gradient of entities in many real networks, material, energy or information of transport on networks is going on along the way of local gradient. The relationship between the function and the structure of network which is driven by the gradient mechanism is discussed in this paper.In the complex gradient network, the transport dynamics depends on the structure and the properties of gradient field of the substrate network. In the current research the correlation between network structure and gradient field are not consider and it is limited to the research of static structure and gradient field. In order to carry out the research, many factors are considered such as the affects of degree correlation, the dynamic changes of gradient field and the correlation between structure and gradient field.1) Unchanging the network structure and the static gradient field, we make a comparative study of the transport efficiency on uncorrelated scale free networks and random networks. We find that the uncorrelated scale free networks can let efficiency transport than the random networks when the average degree larger than2.2) Considering the properties of degree correlation, how the degree correlation on scale free networks affects the transport dynamics driven by the gradient mechanism has been studied. It is observed that the transport efficient is insensitive to the degree correlation intensity for assortative and strongly disassortative scale-free networks, but sensitive for weakly disassortative scale-free networks and increases with an increase for correlation intensity.3) Considering the dynamic characteristic, and taking the node potential as a variable of transport dynamics. We proposed reasonable mechanism for dynamic change of gradient field and researched the relation between network structure and transport dynamics. We can see that the transport capability continues optimizing and reaches its optimal steady state with the increasing evolving time. Furthermore, the scale-free networks are more efficient to transport compared to random networks under the optimizing mechanism.