Understanding control of network spreading from network controllability. (27th September 2017) - Sun, Peng Gang; Ma, Xiaoke
Abstract: How to control the spread of an epidemic or information is a great challenge for us. A dynamic network-based system's structural controllability provides a new way to control spreading with the minimum input of external signals, and the dynamic system is controllable if the signals can drive it from any initial state to any desired final state in finite time. Therefore, we are motivated to develop a new framework by introducing spreading networks (SNs) to describe the spreading pathways from a global view, and we try to understand the control of the spreading by the structural controllability of the SNs. The SNs are transformed from original networks, in which each node is considered as a single spreading origin. The weights of directed links pointing at its direct contacts in the SNs denote the spreading abilities, which can be determined by a new probability function. Furthermore, we also investigate the impact of the dynamics of network structures on the framework. The results show that sparse homogeneous networks with a higher transmission probability tend to trigger a larger scale of diffusion, which is easier to control. We can also see that an epidemic or information is inclined to diffuse easily on the networks with strong community strengths and heterogeneous community sizes. From the structural controllability of the SNs, we observe that driver nodes for the control of the spread tend not to be the nodes located within the core of original networks or those with high-degree. In addition, the scale of diffusion, the number of driver nodes and positions of nodes are highly associated with the degree distribution of the original networks.