Diffusion of Confidential Information on Networks

The development of information and network technology enables us to share information at anywhere and anytime. The social networks on the Internet, for example BBS, SNS, Twitter etc. in the Web, have become the personal network media of information. They are quite useful in information sharing each other. On the other hand, we faced the difficulties in the confidentiality of sensitive content, which have the risk of diffusion of personal or secret information over the Internet. Once the personal and secret information diffuses on the Internet, people on the Internet can know the information anywhere and anytime even in future. This paper presents mathematical models for diffusion phenomena of personal or secret information on the Internet in particular. We investigate the behavior of the models using analytical and computational methods with numerical Monte Carlo simulation. We also consider the structure and dynamics of diffusion on networks constructed by a large number of people with interaction or communication each other. As is well known that social networks have grown rapidly on the Internet. The community on the Internet is in general visible from access logs in servers, rather than that in the real world, so that we can easily analyze the structure and dynamics of the social networks. Not only the element but also the link of a social network determines the behavior of social systems. A network [8] is a set of points (also called vertices or nodes) connected by lines (also called edges or links). We may call complex networks, if the number of points and links is so large that only computational calculation can analyze them. Any system with coupled elements can be represented as a network, so that our world is full of networks[5]. This is a natural generalization of the previous work by Dan [3]. In this paper, we consider the diffusion phenomena of personal or secret information on the variety of networks, such as complete, random, stochastic and scale-free networks.