Research On Model Reduction Of Complex Networks

In recent years,various complex networks have entered almost every aspect of our daily life,which makes the research of complex networks important.However,it is usually difficult to analyse these networks due to their high dimensions.One solution lies in model reduction.We will get a low-dimensional network which is similar to the orginal one by model reduction.And the properties of a network should be remained in model reduction.The truncation method will be used to reduce the order of complex networks in this paper.We firstly consider a truncation method in which only the controlled/observed nodes are reserved.The reduction error is closely related to the number of neighbor nodes of the controlled/observed nodes in this case.And it also reflects the importance of removed nodes in the input-output relationship: nodes close to the controlled/observed nodes are more important in general.Moreover,we propose a new truncation method based on the distance from one node to the controlled/observed nodes.For comparison,we introduce another truncation method based on the input-output centrality.The reduction error of these two methods are fairly similar whether in model networks or in real networks.That is to say,determining the reserved nodes according to their distance from the controlled/observed nodes is reasonable and easy.