Abstract

What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction. Likewise, the brain networks’ complexity arises from interactions beyond pair connections, as it is simplistic to assume that in complex networks state of a link is independently determined only according to its two constituting nodes. This is particularly of note in genetically complex brain impairments, such as the autism spectrum disorder (ASD), which has a surprising heterogeneity in manifestations with no clear-cut neuropathology. Accordingly, structural balance theory (SBT) affirms that in real-world signed networks, a link is remarkably influenced by each of its two nodes’ interactions with the third node within a triadic interrelationship. Thus, it is plausible to ask whether ASD is associated with altered structural balance resulting from atypical triadic interactions. In other words, it is the abnormal interplay of positive and negative interactions that matters in ASD, besides and beyond hypo (hyper) pair connectivity. To address this question, we explore triadic interactions based on SBT in the weighted signed resting-state functional magnetic resonance imaging networks of participants with ASD relative to healthy controls (CON). We demonstrate that balanced triads are overrepresented in the ASD and CON networks while unbalanced triads are underrepresented, providing first-time empirical evidence for the strong notion of structural balance on the brain networks. We further analyze the frequency and energy distributions of different triads and suggest an alternative description for the reduced functional integration and segregation in the ASD brain networks. Moreover, results reveal that the scale of change in the whole-brain networks’ energy is more narrow in the ASD networks during development. Last but not least, we observe that energy of the salience network and the default mode network are lower in ASD, which may be a reflection of the difficulty in dynamic switching and flexible behaviors. Altogether, these results provide insight into the atypical structural balance of the ASD brain (sub) networks. It also highlights the potential value of SBT as a new perspective in functional connectivity studies, especially in the case of neurodevelopmental disorders.

Highlights

  • What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction

  • Analyzing pair interactions between brain regions has revealed fundamental network properties in the last decades, yet in exploring a complex system such as the brain questioning the unavoidable impact of the interactions each of the two regions has with a third region within triadic interrelationships seems plausible

  • The crucial role that weighted signed triadic interactions play in the organization of real-world complex networks which have been widely accepted, is worth considering

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Summary

Introduction

What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction. Graph-theoretic studies are an important foundation for computational modeling of the complex brain networks, and have revealed fundamental properties of their organization and function, in addition to their alterations in brain ­disorders6,7 While all these advances and the potential of graph theory’s perspective is undisputed, a vital question have yet to be asked: Suppose in a signed brain network x, y and z regions are connected, what is the inevitable impact of xz and yz interactions on the sign and weight of the interaction between x and y? Many social scientists have reported that in analyzing large-scale social networks considering the content of interactions, positive (negative) links representing friendship (enmity), contains much promise In this regard, the key role that triadic interactions play in forming the global structure of signed social networks have been strongly ­confirmed. Besides SBT which investigates the structural balance of complex networks through studying triadic interactions, there has been valuable research to explore higher-order interactions in the brain networks based on topological properties as ­well

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