Understanding the structure of complex networks and uncovering the properties of their constituents has been for many decades at the center of study of several fundamental sciences, such as discrete mathematics and graph theory. In the past decade there has been an explosion of interest in complex network data, especially in the fields of biological and social networks. Given the large scale and interconnected nature of these types of networks there is a need for tools that enable us to make sense of these structures.
In this paper we explore how, for a given network, there are a range of emergent dynamic structures that support the different behaviors exhibited by the network’s various state space attractors. For the purpose of our presentation we use a selected Boolean Network, calculate a variety of structural and dynamic parameters, explore the various dynamic structures that are associated with it, and consider the activities (Shannon entropy) associated with each of the network’s nodes when in certain modes/attractors.
This work is a follow-up to past work looking at the relationship between form and function in complex systems, and we hope that such explorations will enable us to develop robust complexity-informed tools to support the wealth of tools associated with Network Theory, with particular emphasis on network dynamics.