Globalization is an important characteristic of the digital age which is based on the informatization of the society as a social-economical and science-technical process for changing the information environment while keeping the rights of citizens and organizations. The key features of the digital age are knowledge orientation, digital representation, virtual and innovative nature, integration and inter-network interactions, remote access to the information resources, economic and social cohesion, dynamic development, etc. The graph theory is a suitable apparatus for discrete presentation, formalization, and model investigation of the processes in the modern society because each state of a process could be presented as a node in a discrete graph with connections to other states. The chapter discusses application of the graph theory for a discrete formalization of the communication infrastructure and processes for remote access to information and network resources. An extension of the graph theory like apparatus of Petri nets is discussed and some examples for objects investigation are presented.