  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 a
conventional 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.
