From brains to science itself, distributed representational systems store and process information about the world. In brains, complex cognitive functions emerge from the collective activity of billions of neurons, and in science, new knowledge is discovered by building on previous discoveries. In both systems, many small individual units—neurons and scientific concepts—interact to inform complex behaviors in the systems they comprise. The patterns in the interactions between units are telling; pairwise interactions not only trivially affect pairs of units, but they also form structural and dynamic patterns with more than just pairs, on a larger scale of the network. Recently, network science adapted methods from graph theory, statistical mechanics, information theory, algebraic topology, and dynamical systems theory to study such complex systems. In this dissertation, we use such cutting-edge methods in network science to study complex distributed representational systems in two domains: cascading neural networks in the domain of neuroscience and concept networks in the domain of science of science. In the domain of neuroscience, the brain is a system that supports complex behavior by storing and processing information from the environment on long time scales. Underlying such behavior is a network of millions of interacting neurons. Many recent studies measure neural activity on the scale of the whole brain with brain regions as units or on the scale of brain regions with individual neurons as units. While many studies have explored the neural correlates of behaviors on these scales, it is less explored how neural activity can be decomposed into low-level patterns. Network science has shown potential to advance our understanding of large-scale brain networks, and here, we apply network science to further our understanding of low-level patterns in small-scale neural networks. Specifically, we explore how the structure and dynamics of biological neural networks support information storage and computation in spontaneous neural activity in slice recordings of rodent brains. Our results illustrate the relationships between network structure, dynamics, and information processing in neural systems. In the domain of science of science, the practice of science itself is a system that discovers and curates information about the physical and social world. For centuries, philosophers, historians, and sociologists of science have theorized about the process and practice of scientific discovery. Recently, the field of science of science has emerged to use a more data-driven approach to quantify the process of science. However, it remains unclear how recent advances in science of science either support or refute the various theories from the philosophies of science. Here, we use a network science approach to operationalize theories from prominent philosophers of science, and we test those theories using networks of hyperlinked articles in Wikipedia, the largest online encyclopedia. Our results support a nuanced view of philosophies of science—that science does not grow outward, as many may intuit, but by filling in gaps in knowledge. In this dissertation, we examine cascading neural networks first in Chapters 2 through 4 and then concept networks in Chapter 5. The studies in Chapters 2 to 4 highlight the role of patterns in the connections of neural networks in storing information and performing computations. The study in Chapter 5 describes patterns in the historical growth of concept networks of scientific knowledge from Wikipedia. Together, these analyses aim to shed light on the network science of distributed representational systems that store and process information about the world.