Considering electronic implications in the Information Society (IS) as a complex system, complexity science tools are used to describe the processes that are seen to be taking place. The sometimes troublesome relationship between the information and communication new technologies and e-society gives rise to different problems, some of them being unexpected. Probably, the Digital Divide (DD) and the Internet Governance (IG) are among the most conflictive ones of internationally based e-Affairs. Admitting that solutions should be found for these problems, certain international policies are required. In this context, data gathering and subsequent analysis, as well as the construction of adequate physical models are extremely important in order to imagine different future scenarios and suggest some subsequent control. In the main text, mathematical modelization helps for visualizing how policies could e.g. influence the individual and collective behavior in an empirical social agent system. In order to show how this purpose could be achieved, two approaches, (i) the Ising model and (ii) a generalized Lotka-Volterra model are used for DD and IG considerations respectively. It can be concluded that the social modelization of the e-Information Society as a complex system provides insights about how DD can be reduced and how the a large number of weak members of the IS could influence the outcomes of the IG.