Information radiation model with across neighbor spread abilities of nodes

Wang Xiao-Yang^{1}, Wang Ying^{1}, Zhu Can-Shi^{2}, Zhu Lin^{1}, Fu Chao-Qi^{1}

1. Equipment Management and Safety Engineering College, Air Force Engineering University, Xi'an 710051, China;
2. Information Engineering College, Xijing University, Xi'an 710123, China

Information is spread as a kind of energy in the network, and it has the ability to spread to nodes that go beyond the neighbors, that is, the information has a radiation effect. However, most of the studies of information dissemination in complex networks only consider the dissemination between neighbors, ignoring that their neighborhood will also be affected by the information radiation. According to this, we propose a new information radiation model with the ability to communicate across neighbors. Firstly, the concepts of information radiation range and radiation attenuation are put forward by combining the theory of complex network and the radiation theory. Secondly, by proposing the hypotheses and analyzing the information content, the nodes in the network are divided into three states:the radiation state, the known state, and the unknown state with the information amount serving as the criterion. At the same time, the transition rules between node states are defined. Thirdly, a three-layer information radiation network model is established based on the physical layer serving as the network structure, the radiation layer as the information dissemination environment, and the state layer as the radiation state statistics. Then, on the basis of the model, the differential equations of the state changes of the nodes are constructed by using the mean field theory and defining the network statistic such as the nth degree, the average nth degree and the nth degree distribution. By analyzing the mechanism of information radiation, the expression of information radiation threshold is deduced by using the differential equation set. Afterwards, the existence of information radiation threshold is proved in each of NW network, BA network, Jazz network, Net-science network, and E-mail network. And the results of numerical simulation and theoretical analysis are well fitted, verifying the correctness of theoretical analysis and the validity of the model. Finally, considering the practical situation of the application, the influences of the state transition probability and the radiation attenuation on the information radiation are analyzed in the BA network by using computer simulation. The results show that the radiation attenuation can stabilize the radiation, and the number of nodes in the initial state of radiation can be increased, which will accelerate the demise of the unknown state nodes but will not increase the number of nodes in the steady state. The results show that increasing the attenuation of the radiation can not only increase the number of radiation nodes in steady stage of radiation, but also speed up the demise of unknown state nodes. And increasing the state transition probability α or γ will affect only the number of the radiation nodes in the initial stage of radiation, also accelerate the demise of the unknown state nodes but will not increase the number of radiation nodes in steady stage of radiation. The analyses of the state transition probability between nodes and the radiation attenuation also prove the correctness of the theoretical analysis.

Wang Xiao-Yang,Wang Ying,Zhu Can-Shi et al.. Information radiation model with across neighbor spread abilities of nodes[J]. Acta Physica Sinica, 2017, 66(3):
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doi:10.7498/aps.66.038901.