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...

Neuronal signalling and communication underpin virtually all aspects of brain activity and function. Network science approaches to modelling and analysing the dynamics of communication on networks have proved useful for simulating functional brain connectivity and predicting emergent network states. This Review surveys important aspects of communication dynamics in brain networks. We begin by sketching a conceptual framework that views communication dynamics as a necessary link between the empirical domains of structural and functional connectivity. We then consider how different local and global topological attributes of structural networks support potential patterns of network communication, and how the interactions between network topology and dynamic models can provide additional insights and constraints. We end by proposing that communication dynamics may act as potential generative models of effective connectivity and can offer insight into the mechanisms by which brain networks transform and process information.

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.

Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system's dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (“routing”), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (“diffusion”). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology.

Computational analysis of communication efficiency of brain networks often relies on graph-theoretic measures based on the shortest paths between network nodes. Here, we explore a communication scheme that relaxes the assumption that information travels exclusively through optimally short paths. The scheme assumes that communication between a pair of brain regions may take place through a path ensemble comprising the k-shortest paths between those regions. To explore this approach, we map path ensembles in a set of anatomical brain networks derived from diffusion imaging and tractography. We show that while considering optimally short paths excludes a significant fraction of network connections from participating in communication, considering k-shortest path ensembles allows all connections in the network to contribute. Path ensembles enable us to assess the resilience of communication pathways between brain regions, by measuring the number of alternative, disjoint paths within the ensemble, and to compare generalized measures of path length and betweenness centrality to those that result when considering only the single shortest path between node pairs. Furthermore, we find a significant correlation, indicative of a trade-off, between communication efficiency and resilience of communication pathways in structural brain networks. Finally, we use k-shortest path ensembles to demonstrate hemispherical lateralization of efficiency and resilience.