Coevolving between structure and dynamics of growing networks

Phenomenon of people with awareness of disseminating new information exists generally in social networks. In that case, people who have known the information would be likely to tell those whom haven't known it. This progress could be regarded as the structure of networks coevolves with disseminating behavior. For investigating the interaction relationship between the structure and dynamics of growing networks, a model is proposed by depicting new information dissemination on the growing networks. At every step, a new node with several edges are added into the network by preferential rule proposed by BA model. By contrast, the range of preferential attachment of the new node is determined by the state of the old node which generating from the progress of information disseminating on the network. The analytical and numerical results show that the interaction between degree distribution and state of nodes becomes unobvious with time coevolving. Statistical property of propagation is affected by number of new edges adding at every step. Emerging of transition of density of nodes which have acquired the information implies that there always exists some nodes not knowing the information.