Review TRENDS in Cognitive Science Vol8 No.9 September 2004 423 tasks and within different locations of the brain.In a size distribution following a power law /611.Importantly ontrast to other iticalitoronndrtoei maxima nforma tran of b an absence of hierarchical organization between criticality and mplexity or specific structura ations to rive fu 11 tions could contribute toan artifac Structural Equation Modeling (SEM,15,64,65))or,more tual recently. Dynami Causal Modeling (DCM,[66))have Despit measures of cau ality might allo the extraction a the relative sca rcity of structural connection data for the (see Bo underlying human cognition ationship between structural connectivity and on:links between a structura substrate complex networks and cognition nal ennes Hig mammalia which al n of mple nization quantitatively be captured usin multivariate and hie ected system .These principles refle ca tic an ura level of complexity ed as the funct al segregatio nal integratio 16 etw n and cog tion ill (modularity)and functional inte tion [33 gration nd tra er c 'dynamic core a potential neural correlate of higher and the occurrence of highly 9 conn patter att pped th are the poten ent con erated -o 34,361 ex tend to follow functional subdivision of thes ifferen of neuronal dyna brains [32. 381.The s of areas delineated by clu ng are also ing wiring gth and structural cluste ing shape east som al ac ivity of hig on pa nts.Bu wocorticalareasae.areadyve7yshortfpicleicl conn ity patte (stru areas connecte or via juat one attribut clus d architecture high e ear why direct conn ons betw areas within possibly metastabl dynami tates (591,and an abun- ster p de add ional benefit The ent al su s that the continual inte ough they might be helpful to grationandredietributionofng conal impul sents eliminate noise from irrelevant rces migh many inte erfere s to task avalanches.In the critical reg the branching n idea ex ssed in the context of co [68).Im pikes ig the f de s of edge s or node riggering event causes a lo g chain of spikes that neithe lar (ma atching)afferent and efferent c out no wsexplosively Apart L at or near criticality.g stems is ideal for ating a balance tasks and within different locations of the brain. In contrast to other biological networks [53], the relative independence of clustering and degree of individual nodes in these examples of brain functional networks indicated an absence of hierarchical organization. Using correlations to derive functional brain networks from fMRI datasets has several known limitations. Transitivity in correlations could contribute to an artifac￾tual increase in the clustering coefficient, suggesting the use of more stringent correlation measures such us partial directed coherence (PDC, [54]). The use of PDC or other measures of causality might allow the extraction and analysis of effective networks (see Box 2) associated with human cognitive function. Relationship between structural connectivity and functional dynamics Neural dynamics unfolding within a structural substrate gives rise to patterns of functional and effective connec￾tivity (Box 2). These patterns exhibit characteristic features of segregation and integration, which can quantitatively be captured using multivariate and hier￾archical information-theoretical measures [16,33,34]. Optimization analyses have demonstrated that a high level of complexity (defined as the co-expression of functional segregation and functional integration [16]) is strongly associated with the emergence of small-world attributes, high proportions of CYCLES and minimized wiring length in structural connection patterns [33]. Such architectures also promote high levels of information integration [55] and the formation of an integrated ‘dynamic core’, a potential neural correlate of higher cognition and consciousness [56,57]. The relation of structural connectivity patterns to resulting neuro-dynamical states has been investigated in detailed computer simulations of cortical networks with heterogeneous [58] and spatially patterned [36] connec￾tion topologies. Different connection topologies generated different modes of neuronal dynamics [34,36]. Locally clustered connections with a small admixture of long￾range connections exhibited robust small-world attributes [35,36], while conserving wiring length, and gave rise to functional connectivity of high complexity with spatially and temporally highly organized patterns. These compu￾tational studies suggest the hypothesis that only specific classes of connectivity patterns (structurally similar to cortical networks) support short wiring, small-world attributes, clustered architectures, high complexity, and possibly metastable dynamical states [59], and an abun￾dance of dynamical transients [60]. A recent proposal suggests that the continual inte￾gration and redistribution of neuronal impulses represents a critical branching process ([61]; see also [62,63]), giving rise to sequences of propagating spikes forming neuronal avalanches. In the critical regime, the branching par￾ameter expressing the ratio of descendant spikes from ancestor spikes is found to be near unity, such that a triggering event causes a long chain of spikes that neither dies out quickly (subcriticality) nor grows explosively (supercriticality). Slice preparations of rat cortex operate at or near criticality, generating neuronal avalanches with a size distribution following a power law [61]. Importantly, criticality is found to be associated with maximal information transfer [61] and thus high efficacy of neuronal information processing. The relationship between criticality and complexity or specific structural connection patterns is still unknown. Within functional brain imaging, approaches such as Structural Equation Modeling (SEM, [15,64,65]) or, more recently, Dynamic Causal Modeling (DCM, [66]) have successfully related brain activation patterns to a chan￾ging functional ‘load’ of structural connections. Despite the relative scarcity of structural connection data for the human brain, these approaches have great potential for revealing distributed functional and effective networks underlying human cognition. Conclusion: links between complex networks and cognition Highly evolved neural structures like the mammalian cerebral cortex are complex networks that share several general principles of organization with other complex interconnected systems. These principles reflect systema￾tic and global regularities in the structural interconnec￾tions and functional activations of brain areas. The work reviewed in this article has suggested some emerging links between network organization and cognition, illu￾minating the structural basis for the coexistence of functional segregation (modularity) and functional inte￾gration, for the rapid generation and transfer of infor￾mation, and for the robustness of brain networks and their failure following damage. Small-world attributes and the occurrence of highly clustered connection patterns appear to represent a general organizational principle found throughout many large-scale cortical networks. What are the potential functional implications of this mode of connectivity? The connectivity clusters found in cat and rhesus monkey cortex tend to follow functional subdivisions of these brains [32,38]. The groups of areas delineated by cluster￾ing are also broadly similar to clusters of semi-functional, neuronographic interactions [67]. Thus, it appears that structural clustering shapes at least some cortical acti￾vation patterns. Clustering implies short path lengths between cluster elements. But path lengths between any two cortical areas are already very short (typically, cortical areas are connected directly or via just one or two intermediate areas [32,33]), so it is not immediately clear why direct connections between areas within a cluster provide additional benefits. The answer may have to do with the signal transformations that are carried out by cortical areas. Although they might be helpful to eliminate noise from irrelevant sources, too many inter￾mediate transformations might interfere with the capacity of brain areas to cooperate on a specialized task (an idea expressed in the context of consciousness [68]). In addition, failures of edges or nodes within clusters can be compensated for more easily, as nearby nodes share similar (matching) afferent and efferent connections. Apart from functional cooperation, clustering might achieve three main purposes. First, the distributed cluster structure of cortical systems is ideal for creating a balance Review TRENDS in Cognitive Sciences Vol.8 No.9 September 2004 423 www.sciencedirect.com