A diffusion perspective on temporal networks: A case study on a supermarket

• Temporal network is understood from a perspective of diffusion process.
• Group IDs are used to represent trajectories of a temporal network.
• The supermarket evolves in a strong order, rather than a complete random.

From a large amount of records, one can extract behavioral characteristics of a social system at different scales. Theoretically, it can help us to know how the global behavior of a social system is formed from individual activities. Practically, it can be used to optimize and even to control the social system. Complicated relationships between the individuals form a network, which evolves with time. The behavior of the system can be accordingly understood in the framework of temporal network. In the present paper, instead of focusing on microscopic structures, we develop a framework to investigate temporal networks from the viewpoint of diffusion process, in which each snapshot network is divided into groups and the ID number of the group a node belongs to is used to measure its state. By this way trajectories of the nodes form an ensemble of realizations of a stochastic process. As an illustration, we investigate the diffusion behavior of a supermarket. One can find that with the increase of time the customers cluster and separate into different groups. Meanwhile, the system evolves in a significant order way, instead of a complete random one.