A new local-world evolving network model

In some real complex networks, only a few nodes can obtain theglobal information about the entire networks, but most of the nodesown only local connections therefore own only local information ofthe networks. A new local-world evolving network model is proposedin this paper. In the model, not all the nodes obtain local networkinformation, which is different from the local world network modelproposed by Li and Chen (LC model). In the LC model, each node hasonly the local connections therefore owns only local informationabout the entire networks. Theoretical analysis and numericalsimulation show that adjusting the ratio of the number of nodesobtaining the global information of the network to the total numberof nodes can effectively control the valuing range for the power-lawexponent of the new network. Therefore, if the topological structureof a complex network, especially its exponent of power-law degreedistribution, needs controlling, we just add or take away a fewnodes which own the global information of the network.