Mirror nodes in growing random networks

In this article, we consider mirror nodes, which are widely used to reduce local burden, and present two models that are practical for the Internet and probably some other networks. One model introduces an upper limit to the number of links that a node can have, beyond which the node will share the total links with a newly introduced one. Similarly, in the second model, if the number of links exceeds a limit, a new node will be introduced. Unlike the first model, the new node shares with the old one the chance of receiving new links but not the existing links. These models are analytically treated, and from the degree distribution, we can see that the number of nodes with medium links (half the upper limit) increases at the expense of the loss of highly connected nodes. By reducing the burden, this may improve the robustness of the networks.