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...

Network studies of human brain structural connectivity have identified a specific set of brain regions that are both highly connected and highly central. Recent analyses have shown that these putative hub regions are mutually and densely interconnected, forming a "rich club" within the human brain. Here we show that the set of pathways linking rich club regions forms a central high-cost, high-capacity backbone for global brain communication. Diffusion tensor imaging (DTI) data of two sets of 40 healthy subjects were used to map structural brain networks. The contributions to network cost and communication capacity of global cortico-cortical connections were assessed through measures of their topology and spatial embedding. Rich club connections were found to be more costly than predicted by their density alone and accounted for 40% of the total communication cost. Furthermore, 69% of all minimally short paths between node pairs were found to travel through the rich club and a large proportion of these communication paths consisted of ordered sequences of edges ("path motifs") that first fed into, then traversed, and finally exited the rich club, while passing through nodes of increasing and then decreasing degree. The prevalence of short paths that follow such ordered degree sequences suggests that neural communication might take advantage of strategies for dynamic routing of information between brain regions, with an important role for a highly central rich club. Taken together, our results show that rich club connections make an important contribution to interregional signal traffic, forming a central high-cost, high-capacity backbone for global brain communication.connectome | graph | tractography I ntegrative brain function depends on neuronal signaling within a complex network of connections linking brain regions (network nodes), the human connectome (1-3). A large proportion of cortico-cortical axonal connections link neurons locally through means of intracortical (gray matter) and short-range white matter axons (4, 5). In contrast, only a small fraction of axonal connections are involved in global communication between distant parts of the network. This long-distance corticocortical connectivity, accessible on the macroscopic scale to noninvasive diffusion imaging and tractography, is the primary focus of our study. Not all brain regions contribute equally to the global structure of the network. So-called "brain hubs" display an above-average level of connectivity and are more centrally embedded (6-11). In addition to being individually highly connected ("rich"), brain hubs exhibit a strong tendency to link to each other, forming a structural core (6) or "rich club" (7). A rich club is defined as a subset of nodes maintaining a large number of connections across the network (i.e., high degree) while at the same time forming mutual connections with a density significantly greater than expected on the basis of their degree alone (12, 13). The brain's cortical rich club was recently shown to consist of a sel...

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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.

The evaluation of the individual “fingerprint” of a human functional connectome (FC) is becoming a promising avenue for neuroscientific research, due to its enormous potential inherent to drawing single subject inferences from functional connectivity profiles. Here we show that the individual fingerprint of a human functional connectome can be maximized from a reconstruction procedure based on group-wise decomposition in a finite number of brain connectivity modes. We use data from the Human Connectome Project to demonstrate that the optimal reconstruction of the individual FCs through connectivity eigenmodes maximizes subject identifiability across resting-state and all seven tasks evaluated. The identifiability of the optimally reconstructed individual connectivity profiles increases both at the global and edgewise level, also when the reconstruction is imposed on additional functional data of the subjects. Furthermore, reconstructed FC data provide more robust associations with task-behavioral measurements. Finally, we extend this approach to also map the most task-sensitive functional connections. Results show that is possible to maximize individual fingerprinting in the functional connectivity domain regardless of the task, a crucial next step in the area of brain connectivity towards individualized connectomics.

Increasingly detailed data on the network topology of neural circuits create a need for theoretical principles that explain how these networks shape neural communication. Here we use a model of cascade spreading to reveal architectural features of human brain networks that facilitate spreading. Using an anatomical brain network derived from high-resolution diffusion spectrum imaging (DSI), we investigate scenarios where perturbations initiated at seed nodes result in global cascades that interact either cooperatively or competitively. We find that hub regions and a backbone of pathways facilitate early spreading, while the shortest path structure of the connectome enables cooperative effects, accelerating the spread of cascades. Finally, competing cascades become integrated by converging on polysensory associative areas. These findings show that the organizational principles of brain networks shape global communication and facilitate integrative function.

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.