The development of new technologies for mapping structural and functional brain connectivity has led to the creation of comprehensive network maps of neuronal circuits and systems. The architecture of these brain networks can be examined and analyzed with a large variety of graph theory tools. Methods for detecting modules, or network communities, are of particular interest because they uncover major building blocks or subnetworks that are particularly densely connected, often corresponding to specialized functional components. A large number of methods for community detection have become available and are now widely applied in network neuroscience. This article first surveys a number of these methods, with an emphasis on their advantages and shortcomings; then it summarizes major findings on the existence of modules in both structural and functional brain networks and briefly considers their potential functional roles in brain evolution, wiring minimization, and the emergence of functional specialization and complex dynamics.

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The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structural connectivity of the human brain and explore the capacity of these measures to predict resting-state functional connectivity across three independently acquired datasets. We focus on the layout of shortest paths across the network and on two communication measures-search information and path transitivitywhich account for how these paths are embedded in the rest of the network. Search information is an existing measure of information needed to access or trace shortest paths; we introduce path transitivity to measure the density of local detours along the shortest path. We find that both search information and path transitivity predict the strength of functional connectivity among both connected and unconnected node pairs. They do so at levels that match or significantly exceed path length measures, Euclidean distance, as well as computational models of neural dynamics. This capacity suggests that dynamic couplings due to interactions among neural elements in brain networks are substantially influenced by the broader network context adjacent to the shortest communication pathways.connectome | graph theory | network theory | brain connectivity T he topology and dynamics of brain networks are a central focus of the emerging field of connectomics (1). A growing number of studies of human brain networks carried out with modern noninvasive neuroimaging methods have begun to characterize the architecture of structural networks (2-4), as well as spatially distributed components (5-7) and time-varying dynamics (8) of functional networks. Although structural connectivity (SC) is inferred from diffusion imaging and tractography, functional connectivity (FC) is generally derived from pairwise correlations of time series recorded during "resting" brain activity, measured with functional magnetic resonance imaging (fMRI). Both networks define a multiplex system (9) in which the SC level shapes or imposes constraints on the FC level. Indeed, mounting evidence indicates that SC and FC are robustly related. Numerous studies have documented strong and significant correlations between the strengths of structural and functional connections at whole-brain (2, 10-13) and mesoscopic scales (14), as well as acute changes in FC after perturbation of SC (15).Although there is ample evidence documenting statistical relationships between SC and FC, the causal role of SC in shaping whole-brain patterns of FC is still only incompletely understood. There are numerous reports of strong FC among brain regions that are not directly structurally connected, an effect that has been ascribed to signal propagation along one or more indirect structural paths (11), or to network-wide contextual influence (16). The present paper builds on two interrelated premises. First, if SC plays a major causal role...

Structure-function relationships are a fundamental principle of many naturally occurring systems. However, network neuroscience research suggests that there is an imperfect link between structural connectivity and functional connectivity in the brain. Here, we synthesize the current state of knowledge linking structure and function in macroscale brain networks and discuss the different types of models used to assess this relationship. We argue that current models do not include the requisite biological detail to completely predict function. Structural network reconstructions enriched with local molecular and cellular metadata, in concert with more nuanced representations of functions and properties, hold great potential for a truly multiscale understanding of the structurefunction relationship. Structure and Function of Brain NetworksThe relationship between structure and function is a central concept in natural sciences and engineering. Consider how the conformation of a protein determines its chemical properties and, ultimately, its biological function. The folding of the protein into a 3D structure promotes interactions among amino acids, allowing the protein to chemically interact with other molecules and endowing it with function. Conversely, disruption of the protein's structure results in loss of function. Tellingly, the protein is said to be denatured, highlighting the idea that changing its structure has fundamentally altered its natural function.

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to different wiring rules combining geometric and a broad range of topological factors. We find that a combination of geometric constraints with a homophilic attachment mechanism can create synthetic networks that closely match many topological characteristics of individual human connectomes, including features that were not included in the optimization of the generative model itself. We use these models to investigate a lifespan dataset and show that, with age, the model parameters undergo progressive changes, suggesting a rebalancing of the generative factors underlying the connectome across the lifespan.