In systems neuroscience, most models posit that brain regions communicate information under constraints of efficiency. Yet, evidence for efficient communication in structural brain networks characterized by hierarchical organization and highly connected hubs remains sparse. The principle of efficient coding proposes that the brain transmits maximal information in a metabolically economical or compressed form to improve future behavior. To determine how structural connectivity supports efficient coding, we develop a theory specifying minimum rates of message transmission between brain regions to achieve an expected fidelity, and we test five predictions from the theory based on random walk communication dynamics. In doing so, we introduce the metric of compression efficiency, which quantifies the trade-off between lossy compression and transmission fidelity in structural networks. In a large sample of youth ( n = 1,042; age 8–23 years), we analyze structural networks derived from diffusion-weighted imaging and metabolic expenditure operationalized using cerebral blood flow. We show that structural networks strike compression efficiency trade-offs consistent with theoretical predictions. We find that compression efficiency prioritizes fidelity with development, heightens when metabolic resources and myelination guide communication, explains advantages of hierarchical organization, links higher input fidelity to disproportionate areal expansion, and shows that hubs integrate information by lossy compression. Lastly, compression efficiency is predictive of behavior—beyond the conventional network efficiency metric—for cognitive domains including executive function, memory, complex reasoning, and social cognition. Our findings elucidate how macroscale connectivity supports efficient coding and serve to foreground communication processes that utilize random walk dynamics constrained by network connectivity. Author Summary Macroscale communication between interconnected brain regions underpins most aspects of brain function and incurs substantial metabolic cost. Understanding efficient and behaviorally meaningful information transmission dependent on structural connectivity has remained challenging. We validate a model of communication dynamics atop the macroscale human structural connectome, finding that structural networks support dynamics that strike a balance between information transmission fidelity and lossy compression. Notably, this balance is predictive of behavior and explanatory of biology. In addition to challenging and reformulating the currently held view that communication occurs by routing dynamics along metabolically efficient direct anatomical pathways, our results suggest that connectome architecture and behavioral demands yield communication dynamics that accord to neurobiological and information theoretical principles of efficient coding and lossy compression.

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work. Author Summary Models of communication in brain networks have been essential in building a quantitative understanding of the relationship between structure and function. More recently, control-theoretic models have also been applied to brain networks to quantify the response of brain networks to exogenous and endogenous perturbations. Mechanistically, both of these frameworks investigate the role of interregional communication in determining the behavior and response of the brain. Theoretically, both of these frameworks share common features, indicating the possibility of combining the two approaches. Drawing on a large body of past and ongoing works, this review presents a discussion of convergence and distinctions between the two approaches, and argues for the development of integrated models at the confluence of the two frameworks, with potential applications to various topics in neuroscience.