The concept of symmetry has played a fundamental role in many of the advances of theoretical physics over the last century. In the physics of complex networks, symmetry also plays an important role. This talk will explore one way that symmetry can be used in Network Science. It will consider Boolean networks, which are simple models of genetic regulatory systems, as well as of a variety of physical, social, and economic systems. They consist of a directed graph with nodes that have binary output states that are heterogeneous functions of the binary input they receive. Each node receives input only from the nodes connected to it by the in‐links of the graph. In general there is a symmetry associated with the dynamics Boolean networks, and different dynamics are characterized by different symmetries. Furthermore, if the networks are evolving then they reflect the symmetry of their evolutionary dynamics. Computer simulations, analytic statistical mechanics, and group theoretic methods will be used to identify the symmetry and to use the results to distinguish various network dynamics. Important symmetry groups will be identified. These groups include the canalization preserving group. Canalization is a form of network robustness that is important for developmental biological systems.
Recent advances in direct construction methods for sampling graphs with arbitrary given degree sequence and the discovery of graphicality transitions in scale‐free networks will also be discussed.