The field of network science presents a superb avenue for exploring the emergent properties of heterogeneous systems. Through a network representation, we can analyze the interactions of a complex system and determine how these interactions lead to unexpected outcomes. In this talk, I will relate the structure of networks to their emergent properties through two projects: network control and network hyperuniformity.

Through network control, we aim to drive a system to a desired state or away from an unwanted state in the most efficient manner. In biological networks, structural information about the system is relatively well known, while dynamical information is typically incomplete. As a result, it is beneficial to understand how to utilize only the structure of a biological network to control the network. We combine the concept of feedback vertex set control with a class of structural metrics we denote as propagation metrics to identify control subsets of the feedback vertex set. We identify subsets of the feedback vertex set that are highly ranked on the propagation metrics, then we implement their control in Boolean biological networks and random Boolean networks built with biological-like structure and show high correlation between a subset’s rank and control. The effectiveness of this control demonstrates that we can find small, effective control sets of biological networks when we only know the system’s structure.

Hyperuniform systems are characterized by the suppression of long-range density fluctuations, and, as a result, exhibit interesting structural properties. We extend this concept to network science by studying the long-range density of different network classes and show that network approaches can effectively differentiate hyperuniform networks. With the introduction of network hyperuniformity, we hope to better understand how the interactions of a system result in an organization that possesses long-range order. Both of the projects in this talk showcase how studying a network can reveal unique, and often unanticipated, information about a system’s emergent properties, and how these properties are fundamentally linked to the network’s structure.