Trends Accumulating evidence from network neuroscience indicates that g depends on the dynamic reorganization of brain networks, modifying their topology and community structure in the service of system-wide flexibility and adaptation. Whereas crystallized intelligence engages easy-to-reach network states that access prior knowledge and experience, fluid intelligence recruits difficult-to-reach network states that support cognitive flexibility and adaptive problem-solving. The capacity to flexibly transition between networks states therefore provides the basis for g – enabling rapid information exchange across networks and capturing individual differences in information processing at a global level. This framework sets the stage for new approaches to understanding the neural foundations of g, examining individual differences in brain network topology and dynamics.

An enduring aim of research in the psychological and brain sciences is to understand the nature of individual differences in human intelligence, examining the stunning breadth and diversity of intellectual abilities and the remarkable neurobiological mechanisms from which they arise. This Opinion article surveys recent neuroscience evidence to elucidate how general intelligence, g, emerges from individual differences in the network architecture of the human brain. The reviewed findings motivate new insights about how network topology and dynamics account for individual differences in g, represented by the Network Neuroscience Theory. According to this framework, g emerges from the small-world topology of brain networks and the dynamic reorganization of its community structure in the service of system-wide flexibility and adaptation.

Spearman’s Enigmatic g 1 Spearman C. ‘General intelligence’ objectively determined and measured. 2 Spearman C. The abilities of man. Research in the psychological and brain sciences has long sought to understand the nature of individual differences in human intelligence, examining the stunning breadth and diversity of intellectual abilities and the remarkable cognitive and neurobiological mechanisms from which they emerge. The foundations of modern research in this effort were established in the early 20th century by Charles Spearman, who developed the correlation method and applied this technique to examine academic achievement within four branches of school study (i.e., English, French, classics, and mathematics) []. 1 Spearman C. ‘General intelligence’ objectively determined and measured. Spearman discovered that correlations in performance reflected characteristics of each discipline, observing that ‘English and French, for instance, agree with one another in having a higher correlation with Classics than with Mathematics’ []. Evidence that all branches of school study were not equally correlated motivated Spearman to conclude that they were influenced, in part, by mental abilities that were specific to each discipline. Beyond identifying the contribution of specific mental abilities, Spearman observed that the correlations among the four branches of school study were always positive. This finding, which is now well-established and named the positive manifold, provided evidence that all cognitive tests measure something in common. Spearman referred to this commonality as the general factor, g, which represents the component of individual differences variance that is common across all tests of mental ability. 1 Spearman C. ‘General intelligence’ objectively determined and measured. 2 Spearman C. The abilities of man. 3 Carroll J.B. Human Cognitive Abilities: A Survey of Factor-Analytic Studies. 4 McGrew K.S.

Wendling B.J. Cattell–Horn–Carroll cognitive-achievement relations: what we have learned from the past 20 years of research. 5 Cattell R.B. Abilities: Their Structure, Growth, and Action. 3 Carroll J.B. Human Cognitive Abilities: A Survey of Factor-Analytic Studies. 6 Deary I.J. The stability of intelligence from childhood to old age. Figure 1 6 Deary I.J. The stability of intelligence from childhood to old age. Hierarchical Structure of General Intelligence. At the level of specific abilities, people differ in scores on individual achievement tests, which are all positively correlated. At the level of broad abilities, strong correlations among tests measuring the same cognitive domain are present. At the level of general ability, people who perform well in one domain also tend to perform well in others, and therefore a general factor (g) can be derived. Adapted, with permission, from These early findings motivated Spearman’s two-factor model which held that performance on tests of mental ability jointly reflect (i) a specific factor, s, that is unique to each test, and (ii) a general factor, g, that is common across all tests []. Contemporary research has further elaborated Spearman’s model to include an intermediate level of broad abilities that account for the variance that is shared across similar domains of cognitive ability. For example, the well-established Cattell–Horn–Carroll theory distinguishes between performance on tests of prior knowledge and experience, referred to as crystallized intelligence, from those that require adaptive reasoning in novel situations, called fluid intelligence []. Taken together, the specific, broad, and general factors of intelligence account for the hierarchical pattern of correlations that are observed among tests of mental ability [] ( Figure 1 ). Spearman’s discoveries ushered in a new era of research on individual differences in human intelligence and uncovered fundamental mysteries about the nature and origins of g that stand as one of the most significant and enduring challenges for modern research in the psychological and brain sciences. Despite the fact that g represents the largest component of the common factor variance, its psychological foundations have remained largely invisible and beyond the reach of further scientific examination. The enigmatic nature of g arises from the fact that it is not a measure of specific knowledge, skills, or strategies for problem-solving. These aspects of task performance are simply a vehicle for the measurement of g. The general factor instead accounts for individual differences in information processing at a global level. Thus, we cannot understand the causal underpinnings of g by appealing to specific cognitive processes or by directly examining the psychological tests from which the general factor is derived. Research on the nature and origins of g must therefore extend beyond psychology to examine the neurobiological mechanisms that shape individual differences in cognitive ability. This Opinion article surveys recent evidence from the burgeoning field of network neuroscience in an effort to elucidate how g – reflected in the positive manifold and the hierarchical pattern of correlations among tests – emerges from individual differences in the network topology and dynamics of the human brain.

Network Perspective 7 Sherrington C.S. Man on His Nature. An enduring vision captured by early research in the neurosciences conceives of the human brain as a dynamic network of interconnected elements – ‘an enchanted loom where millions of flashing shuttles weave a dissolving pattern’ – revealing a complex topology echoed among the stars, ‘as if the Milky Way entered upon a cosmic dance’ []. This celestial view seeks to discover the rich constellation of elements and connections that comprise the human brain at multiple levels of organization – from molecular foundations to higher-level systems – and continues to inspire modern research in the psychological and brain sciences, raising new possibilities for understanding the nature of human intelligence from a network perspective. 8 Bassett D.S.

Sporns O. Network neuroscience. 9 Fornito A.

et al. Fundamentals of Brain Network Analysis. 10 Jensen A.R. Spearman’s g: links between psychometrics and biology. At the frontiers of research in this effort is the interdisciplinary field of network neuroscience [] which applies methods from mathematics, physics, and computer science to enable the formal measurement and modeling of the interactions among network elements, thereby providing a powerful new lens for examining the emergence of global network phenomena. This rapidly developing field holds great promise for advancing research on the nature and origins of g, which represents a global network phenomena par excellence. Indeed, the general factor captures the variance that is common across all tests of mental ability and demonstrates predictive validity across a broad landscape of socially important variables – accounting for academic, professional, economic, and health outcomes []. 11 Thomson G.H. A hierarchy without a general factor. 12 Thomson G.H. The hierarchy of abilities. 13 Thomson G.H. The factorial analysis of human abilities. 14 Deary I.J.

et al. A conversation between Charles Spearman, Godfrey Thomson, and Edward L. Thorndike: The International Examinations Inquiry Meetings 1931–1938 (vol 11, pg 122, 2008). 15 Bartholomew D.J.

et al. Sir Godfrey Thomson: a statistical pioneer. 11 Thomson G.H. A hierarchy without a general factor. 12 Thomson G.H. The hierarchy of abilities. 13 Thomson G.H. The factorial analysis of human abilities. It was therefore shortly after the discovery of g that Spearman’s contemporary, Godfrey Thomson, proposed that the general factor represents a global network phenomenon []. Thomson held that g emerges from the interaction among the many elements of the brain, which he referred to as neural arcs or bonds []. According to Thomson’s Sampling Theory of Mental Ability, each item on an achievement test samples a number of these bonds []. He proposed that the degree of overlap among bonds accounted for the correlation between tests and the resulting positive manifold. Thus, Thomson’s theory was the first to show that Spearman’s discovery of the general factor of intelligence is consistent with a network perspective. 16 van der Maas H.L.

et al. A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. 10 Jensen A.R. Spearman’s g: links between psychometrics and biology. 17 Jensen A.R. The G Factor: The Science of Mental Ability. 18 Pinker S. How could a child use verb syntax to learn verb semantics. 16 van der Maas H.L.

et al. A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. Thomson’s legacy can be found in modern psychological theories which posit that g originates from the mutual interactions among cognitive processes []. Individual differences in g are known to be influenced, for example, by language abilities [], which facilitate a wealth of cognitive, social, and affective processes through mutual interactions (i.e., reciprocal causation) []. The central idea of the Mutualism Model is that change or growth in one aspect of mental ability is (i) partially autonomous (owing to developmental maturation), and is also (ii) based on growth in other areas (owing to the mutual interaction between cognitive processes). By accounting for both the autonomous and interactive nature of cognitive processes, this model is able to explain individual differences in the general factor of intelligence – accounting for the positive manifold and the hierarchical pattern of correlations among tests []. Advances in network neuroscience have further sharpened Thomson’s notion of neural bonds, revealing principles of brain organization that support (i) the modularity of cognitive processes (enabling the autonomy of mental processes), and (ii) the dynamic reorganization of this modular architecture in the service of system-wide flexibility and adaptation (enabling mutual interactions between cognitive processes). The following sections review these principles of brain organization and introduce a Network Neuroscience Theory for understanding individual differences in the general factor of intelligence based on the small-world topology and network dynamics of the human brain. This framework relies upon formal concepts from network neuroscience and their application to understanding the neurobiological foundations of g.

Small-World Network 19 Ramón y Cajal S.

et al. Texture of the Nervous System of Man and the Vertebrates. 19 Ramón y Cajal S.

et al. Texture of the Nervous System of Man and the Vertebrates. 20 Bullmore E.

Sporns O. The economy of brain network organization. Through the incisive lens of his 19th century microscope, Ramón y Cajal observed that ‘the neuron and its various components are simply morphological adaptations governed by the laws of conservation for time, space, and material’ []. These principles provide the modern foundation for understanding the organization of the human brain, which is fundamentally designed for efficiency – to minimize the cost of information processing while maximizing the capacity for growth and adaptation []. 21 Latora V.

Marchiori M. Efficient behavior of small-world networks. 22 Barbey A.K.

et al. Network topology and dynamics in traumatic brain injury. 23 Simon H. The architecture of complexity. 24 Bassett D.S.

Gazzaniga M.S. Understanding complexity in the human brain. Minimization of cost is achieved by dividing the cortex into anatomically localized modules, composed of densely interconnected regions or nodes. The spatial proximity of nodes within each module reduces the average length of axonal projections (conservation of space and material), thereby increasing signal transmission speed (conservation of time) and promoting local efficiency []. This compartmentalization of function enhances robustness to brain injury by limiting the likelihood of global system failure []. Indeed, the capacity of each module to function and modify its operations without adversely effecting other modules enables cognitive flexibility and therefore confers an important adaptive advantage []. Crucially, however, the deployment of modules for coordinated system-wide function requires a network architecture that also enables global information processing. Local efficiency is therefore complemented by global efficiency, which reflects the capacity to integrate information across the network as a whole and represents the efficiency of the system for information transfer between any two nodes. This complementary aim, however, creates a need for long-distance connections that incur a high wiring cost. Thus, an efficient design is achieved by introducing competing constraints on brain organization, demanding a decrease in the wiring cost for local specialization and an opposing need to increase the connection distance to facilitate global, system-wide function. 25 Deco G.

et al. Rethinking segregation and integration: contributions of whole-brain modelling. Figure 2 20 Bullmore E.

Sporns O. The economy of brain network organization. Small-World Network. Human brain networks exhibit a small-world topology that represents a parsimonious balance between a regular brain network, which promotes local efficiency, and a random brain network, which enables global efficiency. Adapted, with permission, from These competing constraints are captured by formal models of network topology [] ( Figure 2 ). Local efficiency is embodied by a regular network or lattice in which each node is connected to an equal number of its nearest neighbors, thus supporting direct local communication in the absence of long-range connections. By contrast, global efficiency is exemplified by a random network in which each node connects on average to any other node, including connections between physically distant regions. 26 Bassett D.S.

Bullmore E. Small-world brain networks. 27 Bassett D.S.

Bullmore E.T. Small-world brain networks revisited. 28 Watts D.J.

Strogatz S.H. Collective dynamics of ‘small-world’ networks. 29 Sporns O.

et al. Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. 30 Sporns O.

et al. Connectivity and complexity: the relationship between neuroanatomy and brain dynamics. 31 Robinson P.A.

et al. Dynamical reconnection and stability constraints on cortical network architecture. 16 van der Maas H.L.

et al. A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. Recent discoveries in network neuroscience suggest that the human brain balances these competing constraints by incorporating elements of a regular and random network to create a small-world topology []. A small-world network embodies (i) short-distance connections that reduce the wiring cost (high local clustering) as well as (ii) long-distance connections that provide direct topological links or short-cuts that promote global information processing (short path length). Together, these features enable high local and global efficiency at relatively low cost, thus providing a parsimonious architecture for human brain organization [] and capturing the modular (autonomous) and global (interactive) network topology that is essential to general intelligence []. 32 He Y.

et al. Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. 33 Eguiluz V.M.

et al. Scale-free brain functional networks. 34 Achard S.

et al. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. 35 Achard S.

Bullmore E. Efficiency and cost of economical brain functional networks. 36 Hagmann P.

et al. Mapping human whole-brain structural networks with diffusion MRI. 37 van den Heuvel M.P.

et al. Efficiency of functional brain networks and intellectual performance. 38 Cole M.W.

et al. Global connectivity of prefrontal cortex predicts cognitive control and intelligence. 39 Stam C.J.

et al. Small-world networks and functional connectivity in Alzheimer’s disease. 40 Stam C.J. Modern network science of neurological disorders. 41 Zuo X.N.

et al. Human connectomics across the life span. 35 Achard S.

Bullmore E. Efficiency and cost of economical brain functional networks. 42 Bassett D.S.

Bullmore E.T. Human brain networks in health and disease. Research in network neuroscience has consistently observed that the topology of human brain networks indeed exemplifies a small-world architecture, and this has been demonstrated across multiple neuroimaging modalities including structural [], functional [], and diffusion tensor MRI []. Emerging neuroscience evidence further indicates that general intelligence is directly linked to characteristics of a small-world topology, demonstrating that individual differences in g are associated with network measures of global efficiency []. Alterations in the topology of a small-world network have also been linked to multiple disease states [], stages of lifespan development [], and pharmacological interventions [], establishing their importance for understanding human health and disease [].

Concluding Remarks 81 Duncan J.

et al. A neural basis for general intelligence. 77 Jung R.E.

Haier R.J. The parieto-frontal integration theory (P-FIT) of intelligence: converging neuroimaging evidence. 83 Kovacs K.

Conway A.R.A. Process overlap theory: a unified account of the general factor of intelligence. Outstanding Questions What are the neurobiological foundations of individual differences in g? Does the assumption that g originates from a primary brain region or network remain tenable, or should theories broaden the scope of their analysis to incorporate evidence from network neuroscience on individual differences in the global topology and dynamics of the human brain? To what extent does brain network dynamics account for individual differences in specific, broad, and general facets of intelligence? To gain a better understanding of this issue, a more fundamental characterization of network dynamics will be necessary. In what respects are ICNs dynamic, how do strong and weak connections enable specific network transformations, and what mental abilities do network dynamics support? How does the structural topology of ICNs shape their functional dynamics and the capacity to flexibly transition between network states? To what extent is our current understanding of network dynamics limited by an inability to measure more precise temporal profiles or to capture higher-order representations of network topology at a global level? How can we facilitate interdisciplinary investigations of human intelligence from a network neuroscience perspective, integrating research across psychology, neuroscience, mathematics, physics, and computer science? What unifying theories and modeling approaches can be applied to integrate research across disciplines to develop a more comprehensive understanding of global network dynamics – from the level of molecules and synapses to neural circuits, networks, and systems? What implications does a network neuroscience perspective have for understanding how intelligence emerges through evolution and development, is cultivated through learning and experience, or is altered through cognitive aging, psychiatric illness, and neurological disease? Network Neuroscience Theory raises new possibilities for understanding the nature and mechanisms of human intelligence, suggesting that interdisciplinary research in the emerging field of network neuroscience can advance our understanding of one of the most profound problems of intellectual life: how individual differences in general intelligence – which give rise to the stunning diversity and uniqueness of human identity and personal expression – originate from the network organization of the human brain. The reviewed findings elucidate the global network architecture underlying individual differences in g, drawing upon recent studies investigating the small-world topology and dynamics of human brain networks. Instead of attributing individual differences in general intelligence to a single brain region [], network [], or the overlap among specific networks [], the proposed theory instead suggests that general intelligence depends on the dynamic reorganization of ICNs – modifying their topology and community structure in the service of system-wide flexibility and adaptation ( Box 1 ). This framework sets the stage for new approaches to understanding individual differences in general intelligence, examining the global network topology and dynamics of the human brain – from the level of molecules and synapses to neural circuits, networks, and systems (see Outstanding Questions). By investigating the foundations of general intelligence in global network dynamics, the burgeoning field of network neuroscience will continue to advance our understanding of the cognitive and neural architecture from which the remarkable constellation of individual differences in human intelligence emerge.

Acknowledgments The work was supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) , via contract 2014-13121700004 to the University of Illinois at Urbana-Champaign (principal investigator: A.K.B.). The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the US Government. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. The author is grateful for the helpful comments provided by Adam Hampshire and two anonymous reviewers.