Atypical Resting-State EEG Graph Metrics of Network Efficiency Across Development in Autism and Their Association with Social Cognition: Results from the LEAP Study.

Vol.:(0123456789) Journal of Autism and Developmental Disorders https://doi.org/10.1007/s10803-025-06731-0 ORIGINAL ARTICLE Atypical Resting‑State EEG Graph Metrics ofNetwork Efficiency Across Development inAutism andTheir Association withSocial Cognition: Results fromtheLEAP Study E.deJonge1 · P.Garcés2· A.deBildt1· Y.Groen3· E.J.H.Jones4· L.Mason5· R.J.Holt6· H.Hayward5· D.Murphy5· B.Oakley5· T.Charman7· J.Ahmad8· S.Baron‑Cohen6· M.H.Johnson9,10· T.Banaschewski11· S.Durston12· B.Oranje13· S.Bölte14,15,16· J.Buitelaar17,18· The EU‑AIMS LEAP group· P.J.Hoekstra1· A.Dietrich1 Accepted: 27 October 2024 © The Author(s) 2025, corrected publication 2025 Abstract Autism has been associated with differences in functional brain network organization. However, the exact nature of these differences across development compared to non-autistic individuals and their relationship to autism-related social cognition, remains unclear. This study first aimed to identify EEG resting-state network characteristics in autistic versus non-autistic children, adolescents, and adults. Second, we investigated associations with social cognition measures. Analyzing restingstate EEG data from the EU-AIMS Longitudinal European Autism Project, we compared network metrics (global efficiency, clustering coefficient, and small-worldness) between 344 autistic and non-autistic individuals within and across age groups in four frequency bands (delta, theta, alpha, and beta). If significant, we explored their relationships to measures of empathy (empathy quotient), complex emotion recognition [reading the mind in the eyes task (RMET)], and theory of mind (animated shapes task). Compared to their non-autistic peers, autistic adolescents showed lower alpha global efficiency, while autistic adults showed lower alpha clustering and small-worldness. No network differences were observed among children. In adolescents, higher long-range integration was tentatively associated with higher RMET scores; in those with high autistic traits, higher long-range integration related to fewer parent-reported empathic behaviors. No brain-behavior relationships were observed in adults. Our findings suggest subtle differences in network topology between autistic and non-autistic individuals, with less efficient long-range efficiency during adolescence, and less local and overall network efficiency in adulthood. Furthermore, long-range integration may play a role in complex emotion recognition and empathy difficulties associated with autism in adolescence. Keywords Autism spectrum disorder· EEG· Resting state· Graph theory· Social cognition Introduction Autism spectrum disorder (hereafter autism) is a neurodevelopmental condition associated with difficulties in social cognition, such as cognitive empathy (i.e., the ability to understand another’s mental state and to respond with a reciprocal emotion or action; Harmsen, 2019; Sucksmith etal., 2013), complex emotion recognition (Baron-Cohen etal., 2001; Oakley etal., 2016), and theory of mind (ToM; i.e., the ability to attribute mental states to oneself and others; Velikonja etal., 2019; Wilson, 2021). Research suggests that autism is related to atypical resting-state functional connectivity (i.e., synchrony of activity between brain regions; Belmonte etal., 2004; Just etal., 2004). Functional connectivity across and within brain regions is also critical for complex cognitive functions like social cognition, including empathy, complex emotion recognition, and ToM (Müller & Fishman, 2018; Van Overwalle, 2009). However, whether atypical restingstate network connectivity in autism contributes to its associated difficulties in social cognition remains understudied. Where most studies on resting-state functional connectivity in autism have used functional magnetic resonance imaging (fMRI; for review see Lau etal., 2019), electroencephalography (EEG) offers several advantages. As opposed to fMRI, it directly measures neuronal activity, provides higher Members of The EU-AIMS LEAP group are listed in the Acknowledgments section. Extended author information available on the last page of the article Journal of Autism and Developmental Disorders temporal resolution (allowing studying networks within different frequency bands), and is less invasive (greater ease of use with a diverse range of participants). EEG studies, utilizing a variety of connectivity measures, have generally indicated reduced long-range connectivity in autistic compared to non-autistic individuals across age, while differences in short-range connectivity have been less established (for review see O’Reilly etal., 2017). Currently, the exact nature of EEG network connectivity in autism remains incompletely understood, especially across different connectivity measures, frequency bands, and developmental stages (O’Reilly etal., 2017; for review on MRI and MEG see Picci etal., 2016). A recent study on functional connectivity in autism using resting-state EEG data from the Longitudinal European Autism Project (LEAP) did not find autism-related differences as quantified by the weighted Phase Lag Index [wPLI; a measure of phase synchronization between EEG signals discarding zero-lag synchronization (Vinck etal., 2011)] in children, adolescents, or adults (Garcés etal., 2022). Yet, compared to overall connectivity measures, applying graph theory to resting-state EEG functional connectivity data allows for a more detailed quantification of functional network characteristics. It provides a mathematical framework to study complex networks and the information flow in them. By quantifying properties including network topology, efficiency, and organization, graph theory can facilitate a more comprehensive understanding of connectivity (Bullmore & Sporns, 2009; Rubinov & Sporns, 2010). The few EEG resting state connectivity studies that have used graph theory to study autism have yielded inconsistent results so far. Some studies have reported lower network connectivity in autistic compared to non-autistic individuals through less efficient long-range network connectivity (as reflected by increased path length or decreased global efficiency), reduced local information processing (as reflected by decreased clustering coefficients), and/or architectures less typical of small-world networks (i.e., suboptimal equilibrium between long-range and local information processing) across autistic toddlers (Boersma etal., 2013), children (Zeng etal., 2017), and adults (Barttfeld etal., 2011). Moreover, in an adult neurotypical sample, autistic traits were associated with deviations from the optimal smallworld network structure (Barttfeld etal., 2013). However, opposite patterns of decreased path length in autistic children (Zeng etal., 2017) and increased local connectivity in autistic children and young adults (Peters etal., 2013) have also been reported. Regarding neurotypical development, a further differentiation of long-range connectivity across age would be expected (Edde etal., 2021), however, patterns are currently unclear regarding graph metrics in autistic individuals as both underand overconnectivity appear plausible (O’Reilly etal., 2017). Also, studies in adolescents are lacking as are studies simultaneously investigating multiple age periods (Picci etal., 2016). Moreover, the examined frequency bands varied between studies, likely giving rise to conflicting findings (Barttfeld etal., 2011; Boersma etal., 2013; Peters etal., 2013). This highlights the need to evaluate graph metrics across multiple frequency bands within the same study. Most importantly, however, sample sizes were generally small (ranging from 10 to 21 individuals with autism; Barttfeld etal., 2011; Boersma etal., 2013; Peters etal., 2013; Zeng etal., 2017), which may have biased the results. Given the heterogeneous nature of autism, larger samples are needed to be able to meaningfully capture this diversity. In sum, EEG resting-state graph metric studies in larger samples considering multiple frequency bands and developmental stages are needed. Addressing these elements together in one study using consistent methodologies will provide a more comprehensive view of brain connectivity in autism, which is difficult to achieve between studies with differing analysis techniques. Additionally, these investigations could provide insight into context-independent markers of the social-cognitive characteristics associated with autism (Picci etal., 2016). While the EEG network properties have been linked to various cognitive domains, e.g., IQ (Zakharov etal., 2020), memory performance (Vecchio etal., 2016), and literacy skills (Lui etal., 2021), it remains unknown whether network atypicalities associated with autism are related to its social cognitive characteristics. To our knowledge, this is the first study to investigate the link between atypical restingstate EEG graph metrics and measures of empathy, complex emotion recognition, and ToM in autism. The aim of the current paper was twofold: (1) to identify autism-related EEG resting-state characteristics of network efficiency across different developmental stages in a sizeable sample, and (2) to investigate their relationship with social cognition measures. We investigated differences between autistic and non-autistic individuals in three resting-state EEG network metrics that have previously been indicated in autism (path length/global efficiency, clustering, and small-worldness), across four canonical frequency bands (delta, theta, alpha, beta), and three age groups (children, adolescents, and adults), using data from the EU-AIMS LEAP study, a large multicenter initiative aimed at identifying biomarkers in autism (Charman etal., 2017; Loth etal., 2017). We also examined dimensional relationships between graph metrics and autistic trait scores across autistic and non-autistic participants (Constantino & Todd, 2003). We further investigated whether autism-related network structures were predictive of parent-reported empathy and performance on social cognition tests, in order to provide a more meaningful interpretation of autism-related connectivity patterns. As noted above, in light of changes in brain maturation across development, with typically stronger local efficiency Journal of Autism and Developmental Disorders (clustering) in childhood and increasing long-range and overall efficiency (global efficiency, small-worldness) across age (Edde etal., 2021), we expected developmental differences in autism-related connectivity suggesting delayed or atypical development. Also, we hypothesized lower network efficiency to be associated with lower empathy, complex emotion recognition, and ToM scores. Methods Participants The sample was part of the EU-AIMS LEAP cohort (Charman etal., 2017; Loth etal., 2017). Data were acquired at five sites: Mannheim Central institute of Mental Health (CIMH, Germany), King’s college London (KCL, United Kingdom), University Nijmegen Medical Centre (RUNMC, Netherlands), University Campus BioMedico (UCBM, Italy), and University Medical Centre Utrecht (UMCU, Netherlands). Participants were recruited from a variety of sources including existing volunteer databases, existing research cohorts, clinical referrals from local outpatient centers, special needs schools, mainstream schools and local communities (Charman etal., 2017). The LEAP study was approved by the local ethical committees of the participating centers. Written informed consent was obtained from all participants and/or their legal guardians (for participants under 18years of age). LEAP participants were included in three age groups [children (6–11years), adolescents (12–17years), and adults (18–31years)], aligning with transitions between formal education (i.e., from primary to secondary school at age 12, and the end of formal education at age 18). Of all LEAP participants without intellectual disability (N = 653), we selected those who had clean EEG data (for criteria see SI2) with an accompanying MRI head model, as well as parent-reported (children and adolescents) or self-reported (adults) autistic trait scores available, resulting in a sample of 344 individuals. The groups of included and excluded autistic participants differed at the uncorrected group level on SRS-2 raw score and ADI-R social and communication subscales, with higher symptomatology in the excluded group. Of the non-autistic participants, the excluded group had higher SRS-2 raw scores (see SI1 for more details). This might be expected since participants with higher symptom expression are less likely to be able to comply with instructions, and more likely to cause artifacts during EEG and MRI acquisition by moving. Autistic individuals had an existing clinical diagnosis of ASD according to DSM-IV (American Psychiatric Association, 1994), DSM-IV-TR (American Psychiatric Association, 2000), DSM-5 (American Psychiatric Association, 2013), or ICD-10 criteria (World Health Organization, 2013). Autism characteristics were assessed using the Autism Diagnostic Observation Schedule second edition (ADOS-2; Lord etal., 2012) and the Autism Diagnostic Interview-Revised (ADIR; Rutter etal., 2003). We did not exclude participants with a clinical autism spectrum diagnosis who did not reach cutoff scores on these instruments or the SRS-2, since clinical judgement has shown to be more stable than diagnostic instrument scores alone (Charman & Gotham, 2013; Lord etal., 2006). Non-autistic participants (the comparison group) had t-scores below 70 on the Social Responsiveness Scale second edition (SRS-2; Constantino & Gruber, 2012), and had no parentor self-reported psychiatric conditions. Participants were allowed to take their usual medication at the time of the study. Clinical andCognitive Measurements All measures were collected as part of a multimodal assessment within LEAP. Cognitive and EEG measures were taken on different assessment days that took place within 4weeks of one another. Questionnaires were filled out online prior to, during, or shortly after the assessment days. All social cognition measures within LEAP that were stand-alone (e.g., not assessed within neuroimaging environments) were included in the current study. We used the standard version of the SRS-2 as a dimensional measure of autistic traits. The SRS-2 is a well-validated, 65-item screening instrument that assesses autistic traits over the past six months with subscales on social communication, awareness, motivation, social cognition, and behavior flexibility (Constantino & Gruber, 2012). Each item poses a statement and is scored on a 4-point Likertscale ranging from ‘not true’ to ‘almost always true’, where higher scores indicate more autistic traits. Parent-report forms were used for the child and adolescent groups, while adults self-reported autistic traits [general internal consistency: 0.94—0.96; Cronbach’s alpha of current study: 0.91 (children), 0.90 (adolescents), 0.93 (adults)]. In the current study, raw scores were used as recommended when considering covariates in research settings. IQ was assessed using the Wechsler Abbreviated Scales of Intelligence (Wechsler, 1991, 2003) or Wechsler Intelligence Scale for Children (Wechsler, 1997, 2008). Empathy was measured using the Empathy Quotient (EQ; Wheelwright & Baron-Cohen, 2004). The EQ is a rating scale measuring both cognitive and affective empathy comprising 27 (child version) or 40 (adolescent and adult version) items. Cognitive empathy is the ability to imagine someone else’s mental state, whilst affective empathy is the drive to respond to another person’s mental state with an appropriate emotion. A 4-point Likert scale assesses Journal of Autism and Developmental Disorders statements about real life situations, experiences, and interests where empathizing abilities are required. It has been shown to have good test–retest reliability (Auyeung etal., 2012). Cronbach’s alpha internal consistencies in the present sample were 0.90, 0.94, and 0.91, for children, adolescents, and adults respectively. In LEAP, raw scores were binarized so that answers corresponding to higher empathy were scored 1 and those corresponding to lower empathy were scored 0 (Wright & Skagerberg, 2012). Binary scores were then summed into total scores per participant. Thus, higher scores indicate more empathy. EQ forms were filled out by parents for children and adolescents, while adults used self-report forms. Complex emotion recognition was measured by the Reading the Mind in the Eyes Test (RMET; Baron-Cohen etal., 2001, 2015). The RMET is a well-validated 36-item task with age-appropriate versions for children, adolescents and adults. It requires participants to identify complex emotional expressions from pictures of human eyes and the immediate surrounding facial area by selecting labels that describe emotional states. While the RMET was initially designed to assess ToM ability, growing evidence indicates that it may rather capture complex emotion recognition (Oakley etal., 2016). The RMET has shown good validity across different cultural settings and ages (Doyle-Thomas etal., 2015; Hayward & Homer, 2017; Holt etal., 2014; Lee etal., 2020; Vellante etal., 2013). We used percentage correct scores (the proportion of correctly identified items). ToM skills were measured by the Frith-Happé Animated Shapes Narratives task (Abell etal., 2000). Participants were asked to verbally describe animations of two triangles moving on a screen in three different conditions: (1) moving in a goal-directed fashion (chasing, fighting), (2) moving interactively with implied intentions (coaxing, tricking), or (3) moving randomly. For this study, we used accuracy scores (how accurately did the participant understand the ToM animation?) on the second condition (ToM). We additionally calculated accuracy scores on the third condition (random movement) as a secondary control measure (how accurately did the participant understand that movement was random or purposeless?). All age groups used the same version as supported by a recent meta-analysis that indicated similar task-effects across autistic children and adults (Wilson, 2021). For further details on all measures used, see (Loth etal., (2017). EEG Preprocessing andCalculation ofGraph Metrics Resting-state EEG data were recorded for four minutes (8 blocks of 30s). Blocks alternated between eyes open and eyes closed conditions, in which participants respectively fixated on a physical hourglass or had their eyes closed. In line with previous resting-state studies, the current study used eyes closed data only, minimizing the impact of blink, eye-movement, or saccade artifacts (e.g., Shou etal., 2017), and facilitating a more focused investigation of neural dynamics, given that eyes-open and eyes-closed conditions may yield distinct results (Petro etal., 2022). In short, the resting-state EEG data were preprocessed, source-localized, and split into the four frequency bands of interest [delta (2–4)Hz, theta (4–8)Hz, alpha (8–13)Hz, and beta (13–30) Hz]. Subsequently, wPLI connectivity matrices were constructed per frequency band, per participant. Connectivity matrices were thresholded and binarized for 10 evenly spaced thresholds between 0.05 (preserving only the top 5 percent of weights) and 0.3 (preserving only the top 30 percent of weights (van Wijk etal., 2010). Four graph metrics were extracted from each connectivity matrix. Global efficiency describes the number of edges that are needed to reach other nodes in a network (Rubinov & Sporns, 2010) and higher global efficiency indicates more efficient long-range information integration. Characteristic path length is the inverse of global efficiency. While both metrics describe the same network property, global efficiency is better suited to deal with networks containing unconnected nodes (which are likely to occur) and was therefore our preferred metric to describe global network efficiency (Rubinov & Sporns, 2010). We additionally derived path length as it is commonly used in small-world coefficient calculations (described below). We assumed that if path length and global efficiency yielded similar results, path length could be safely used in small-world coefficient calculations. The average clustering coefficient describes how close neighboring nodes in a network cluster together and a higher clustering coefficient indicates increased segregation (or higher efficiency in local information processing; Rubinov & Sporns, 2010). The small-world coefficient reflects the ratio between normalized clustering and path length, and a higher coefficient indicates higher over-all network efficiency (Rubinov & Sporns, 2010). More details on preprocessing, source localization, graph thresholding, and calculation of graph metrics can be found in the supplementary information (SI2). Statistical Analyses To compare demographic, clinical, and social cognition measures between autistic and non-autistic comparison groups within each age group we used Welch two-tailed t-tests, Chi square tests. Note that all comparisons between autistic and comparison groups were conducted per age group given the respective differences in versions and/or informants of social cognition measures across the age groups. This allowed us to account for possible nonlinear age dependencies (e.g., effects only in adolescents but not children or adults), to explore associations between graph Journal of Autism and Developmental Disorders metrics and social cognition measures and is in line with previous LEAP studies using predefined age groups (Crawley etal., 2020; Haartsen etal., 2022). Where possible (i.e., measures for which the same version and informant were used across all age groups), measures were compared between age groups for autistic and non-autistic individuals separately. To compare graph metrics between the autistic and comparison groups we used linear regression models for each graph threshold within each frequency for children, adolescents, and adults separately, where group was the predictor and the graph metric the dependent variable. Analyses were adjusted for site differences, as well as age (squared), sex, and IQ (all fixed effects), as previous studies suggest associations between the latter three and functional connectivity (e.g., Alaerts etal., 2016; Nentwich etal., 2020; Tarokh etal., 2010). Linear predictors were mean centered before entering the statistical models. To account for multiple comparisons across graph metrics, frequency bands, and thresholds, we adopted a cluster-based approach in which group differences for the graph metrics were considered significant only if results (p < 0.05) were replicated across at least three subsequent thresholds within the same frequency band (van Wijk etal., 2010). Of these, the threshold showing the highest effect size (determined by partial R2) of all successive significant neighbors was selected for subsequent analyses of the relation between graph metrics and social cognition. Traditional application of false discovery rates or equivalents would be inappropriate here because (1) the successive thresholded networks and thus their resulting graph metrics are not independent for each successive network results from adding a few edges to the previous one, and (2) the small-world coefficient is not independent from clustering and path length, as it reflects the ratio between them. We tested whether any identified autism-related graph metric differed between age groups using ANOVA’s (combined with Tukey’s HSD post-hoc tests). To investigate associations between the graph metrics and autistic trait scores (SRS-2) across both autistic and non-autistic participants in a dimensional approach, we used linear regression models where SRS-2 scores were the predictor and the graph metric was the dependent variable, including the same covariates. Densities with significant autistic trait associations were determined using the same cluster-based approach as described above. We additionally tested SRS-2 by group interactions within significant densities to check if associations differ for the autistic and non-autistic groups. To explore associations of the graph metrics (selecting only those that were different between the autistic and comparison groups) with social cognition measures across the total sample of autistic and non-autistic individuals within each age group (as we expected measures to be dimensionally distributed), we used linear regression models including the same covariates as above. We additionally explored interaction effects between graph metrics and SRS-2 scores to see if possible associations depend on autistic traits. A significance threshold of p < 0.05 was applied to all regression models. We present Cohen’s d, η2, or partial R2 effect sizes where appropriate. All statistical analyses were performed in R (version 4.0.4; https:// www.rproje ct. org/) and linear regressions were fitted using the lme4 package (Bates etal., 2015). To evaluate the impact of medication on the results, post-hoc sensitivity analyses were performed on significant models by including medication status as a covariate. Significant models were verified to have normally distributed residuals (visual inspection of QQ plots and Shapiro–Wilk normality tests), which did not show autocorrelation (by Durbin-Watson tests) and no homoscedasticity of error variance (visual inspection); there was also no multicollinearity between predictors (determined by variance inflation factors). Results Demographic andClinical Descriptives Table1 summarizes the main demographics and clinical characteristics of the autistic and comparison groups for each age group. The final sample comprised 184 autistic and 160 non-autistic participants who met our inclusion criteria (for attrition rates see SI3); 86% of 49 autistic children, 97% of 68 autistic adolescents, and 91% of 67 autistic adults scored above the ADOS-2 and/or ADI-R cutoffs, following threshold definitions by Risi etal. (2006), while respectively 14% (7 children), 3% (2 adolescents), and 9% (6 adults) did not reach cut-off thresholds relying on clinical diagnosis alone (for more details and distributions of ADOS-2 scores see SI4). Age (p’s ≥ 0.09), sex (p’s ≥ 0.28), and IQ (p’s ≥ 0.09) did not show statistically significant differences between autistic and comparison groups within any age group. Autistic trait scores as measured by the SRS-2 were significantly higher in all autistic groups compared to the non-autistic groups (p’s ≤ 0.001). When comparing age groups, full-scale IQ scores were lower for the autistic adolescents compared to the autistic children and adults, who did not significantly differ from each other (F(2,181) = 4.42, p = 0.01, η2 = 0.05). Full-scale IQ scores in the comparison groups were also lower for the adolescents compared to the children, but not significantly different from the adults. Child and adult comparison groups did not differ on IQ (F(2,157) = 3.83, p = 0.024, η2 = 0.05). Neither autistic or comparison Journal of Autism and Developmental Disorders Table 1 Demographic, clinical and social cognitive characteristics of the samples Values represent mean (standard deviation) [minimum-maximum]. SRS-2 Social Responsiveness Scale-2 (note that the SRS-2 t-score was used as a selection criterion only for non-autistic participants [t < 70] and not for autistic participants), ADOS-2 Autism Diagnostic Observation Schedule-2, SA Social Affect, CSS Calibrated Severity Scores, RRB Restricted and Repetitive Behaviours, ADI-R Autism Diagnostic Interview Revised, Medication refers to whether or not participant was using medication affecting the brain at the time of the study (antidepressants, antimigraine, antipsychotics, anxiolytics, hypnotics, sedatives, psychostimulants, analgesics, …) Children Adolescents Adults Autistic Comparison Autistic Comparison Autistic Comparison n (female) 49 (18) 43 (18) 68 (16) 56 (19) 67 (21) 61 (17) Age (years) 9.63 (1.39)[6.8–11.9] 9.72 (1.52) [6.9–12.0] 14.8 (1.78) [12.1– 17.9] 15.4 (1.72) [12.2– 18.0] 23.0 (3.46) [18.0– 30.3] 23.1 (3.48) [18.3–31.0] Full-scale IQ 107 (14.3) [77–139] 112 (13.3) [76–142] 100 (14.9) [75–139] 105 (13.3) [77–126] 106 (13.7) [75.6–148] 109 (11.4) [86.0–142] Medication 20 (n = 47) 0 (n = 41) 25 (n = 63) 4 (n = 54) 15 (n = 61) 1 (n = 53) SRS-2 Raw scores 90.6 (31.9)[32–163] 19.0 (13.3)[2–74] 92.0 (28.5) [22–149] 22.1 (16.7)[1–74] 78.5 (30.2) [12–152] 29.5 (14.0)[8–76] t-scores 73.2 (11.6) [49–90] 44.8 (5.24) [37–66] 73.7 (11.2) [45–90] 46.0 (6.60) [38–66] 63.4 (10.6) [40–89] 46.2 (5.00) [39–63] ADOS-2 SA CSS 5.29 (2.33)[1–9] NA 6.42 (2.59)[1–10] (n = 67) NA 5.52 (2.61)[1–10] NA RRB CSS 3.91 (3.09)[1–9] NA 4.49 (2.55)[1–10] (n = 67) NA 4.45 (2.61)[1–10] NA total CSS 4.69 (2.40)[1–10] NA 5.61 (2.74)[1–10] (n = 67) NA 4.78 (2.59)[1–10] NA ADI-R Social 13.9 (7.14) [1–29] (n = 47) NA 17.7 (6.28)[2–29] NA 13.6 (6.17)[0–26] NA Communication 12.3 (5.03) [3–23] (n = 47) NA 14.1 (5.74)[1–26] NA 10.6 (5.33)[0–24] NA RRB 3.91 (3.09) [0–10] (n = 47) NA 4.41 (2.88)[0–12] NA 4.03 (2.63)[0–12] NA Journal of Autism and Developmental Disorders groups significantly differed between age groups on sex (p’s > 0.29) or medication use (p’s > 0.17). Autistic age groups did not differ on clinical characteristics measured by the ADOS-2 (p’s > 0.38) or ADI-R (p’s > 0.29). SRS-2 scores could not be reliably compared between age groups, because of differences in reporters in each age group. Social Cognition Descriptives Table2summarizes the social cognitivecharacteristics of the autistic and comparison groups for each age group.EQ scores were lower for autistic groups compared to the comparison groups for children (t(74.7) = −10.6, p < 0.001, d = −2.19), adolescents (t(102.7) = −14.8, p < 0.001, Cohen’s d = −2.88), and adults (t(104.7) = −7.9, p < 0.001, d = −1.41). RMET scores were lower for autistic groups compared to the comparison groups for adolescents (t(103.8) = −3.0, p = 0.003, d = −0.56) and adults (t(116.0) = −2.7, p = 0.009, d = −0.47), but not children (t(77.2) = −1.23, p = 0.22, d = −0.27). Autistic and comparison groups did not show statistically significant differences in animated shapes ToM or random condition scores for any of the age groups (p’s ≥ 0.13). When comparing age groups, autistic adults scored higher on the animated shapes ToM condition compared to the autistic children and adolescents, who did not significantly differ from each other (F(2,170) = 17.1, p < 0.001, η2 = 0.17). This pattern was similar for the comparison groups, but the non-autistic children scored significantly lower than the adolescents and adults, while non-autistic adolescent and adult groups did not show statistically significant differences (F(2,139) = 4.76, p = 0.01, η2 = 0.06). RMET and EQ scores could not be reliably compared between age groups, because of differences in versions and/or reporters in each age group. Graph Metric Comparisons Between Autistic andNon‑autistic Individuals andAssociations withAutistic Trait Scores Since path length showed similar results as global efficiency for all frequency bands, thresholds, and age groups (SI7), we concluded that it could be reliably used in small-world coefficient calculations. In none of the following analyses did medication status contribute to significant models or results in post-hoc sensitivity analyses (not shown), indicating that taking psychoactive medication had no effect on the present results. Only in the alpha frequency band, graph metrics differed between autistic and comparison groups and were associated with autistic trait scores, but not in the delta, theta, or beta bands. In children, autistic and comparison groups did not significantly differ on any of the graph metrics (Fig.1) and autistic trait scores were not related to graph metrics in the total sample across the autistic and comparison groups (not shown). Group means and standard deviations for each graph metric, frequency band and threshold for each age group can be found in the supplementary information (SI5), additional data are available upon request. In adolescents, however, global efficiency was lower (p < 0.05 at three successive thresholds) for the autistic compared to the comparison group in the alpha band (thresholds 0.16, 0.19, 0.22; Fig.1 and SI5).We selected threshold 0.22 for subsequent associations with social cognition, based on the largest effect size of group (R2 = 0.05). Across both the autistic and comparison groups, lower global efficiency was significantly associated with higher autistic trait scores in adolescents for the same thresholds (0.16, 0.19, and 0.22), and additionally for threshold 0.24 (Fig.2a [visualization of threshold 0.16] and SI6). Effect sizes of autistic trait scores with global efficiency were about twice as high as those for autistic versus comparison group comparisons in global efficiency (R2’s > 0.07). Of the covariates, only site significantly contributed to associations with global efficiency, Table 2 Social cognitive characteristics of the samples Values represent mean (standard deviation) [minimum–maximum]. EQ Empathy Quotient total scores, RMET Reading the Mind in the Eyes Test % correct, AS ToM Animated Shapes accuracy scores on ToM condition, AS random AS accuracy scores on random condition Children Adolescents Adults Autistic Comparison Autistic Comparison Autistic Comparison EQ 13.5 (5.24) [4–27] (n = 47) 23.1 (2.94) [14–27] (n = 38) 14.7 (6.18)[6–35] (n = 56) 31.9 (5.69) [15–39] (n = 49) 21.6 (8.33)[4–39] (n = 64) 31.5 (4.93) [19–39] (n = 54) RMET 58.2 (13.8) [14–86] (n = 42) 61.5 (10.8) [36–82] (n = 41) 54.7 (12.9) [26–89] (n = 60) 61.0 (8.66) [42–78] (n = 51) 65.8 (14.0) [19–89] (n = 64) 71.7 (10.4) [44–89] (n = 60) AS ToM 2.35 (1.47) [0–6] (n = 48) 2.76 (1.38)[0–6] (n = 38) 3.10 (1.64)[0–7] (n = 60) 3.60 (1.65) [0–7] (n = 47) 4.18 (1.84)[0–8] (n = 65) 3.75 (1.67) [0–7] (n = 57) AS random 2.46 (1.17) [0–4] (n = 48) 2.63 (1.40)[0–4] (n = 38) 2.92 (1.42)[0–4] (n = 60) 2.81 (1.26) [0–4] (n = 47) 2.71 (1.34)[0–4] (n = 65) 2.56 (1.36) [0–4] (n = 57) Journal of Autism and Developmental Disorders indicating that participants in London on average had higher global efficiency compared to participants in Mannheim and Nijmegen. In adults, clustering and small-worldness in the alpha band were significantly lower in the autistic group compared to the comparison group (thresholds 0.05, 0.08, and 0.11; Fig.1 and SI5). None of the covariates consistently contributed to the associations. We selected threshold 0.05 for clustering and 0.08 for small-worldness for subsequent associations with social cognition measures (R2 = 0.06 and R2 = 0.05). Across autistic and comparison groups, less clustering was associated with higher autistic trait scores for thresholds 0.08, 0.11 and 0.13 (Fig.2b and SI6). Smallworldness did not reach significance on more than two thresholds, and thus did not show evidence of association with autistic trait scores. Subsequently tested autistic trait scores-by-group interactions were not significant for any of the associations with autistic traits in either adolescents or adults, indicating that associations between autistic trait scores and graph metrics were independent of group status (SI6). Across age groups, autistic groups did not differ in alpha global efficiency. However, non-autistic children on average had higher alpha global efficiency than non-autistic adults, while adolescents did not significantly differ from children or adults in the non-autistic sample (F(2,157) = 4.34, p = 0.01, η2 = 0.05). Further, autistic children on average had higher clustering and small-worldness than autistic adolescents and adults. Autistic adolescents did not significantly differ from autistic adults on clustering (F(2,181) = 10.9, p < 0.001, η2 = 0.11), but had lower small-worldness (F(2,181) = 12.43, p < 0.001, η2 = 0.12). In contrast, comparison age groups did not show statistical differences on clustering or small-worldness, suggesting a stable local efficiency across age. Fig. 1 Comparisons of graph metrics between autistic and non-autistic groups in the alpha band. Group means per threshold are shown for each graph metric per age group for the alpha frequency band. Vertical bars represent standard errors. *p < .05 Journal of Autism and Developmental Disorders Associations Between Autism‑Related Graph Metrics andSocial Cognition In the total sample of adolescents (autistic and non-autistic individuals together), global efficiency was not predictive of EQ or animated shapes ToM scores, but was tentatively associated with RMET scores [partial R2 = 0.04, p = 0.053 (Table3)], suggesting that higher global efficiency is associated with better RMET performance. Age and IQ significantly contributed to this model, indicating that RMET performance increases with age and IQ. The site contrast London-Utrecht was also significant, i.e., participants in London on average scored higher on the RMET compared to participants in Utrecht when adjusting for the other predictors. In the model predicting animated shapes ToM scores, IQ was a significant contributor, i.e., animated shapes ToM Fig. 2 Associations between graph metrics and autistic trait scores across autistic and non-autistic groups. SRS-2 Social Responsiveness Scale-2. Illustration of association between global efficiency in adolescents and clustering in adults with autistic traits scores for those densities that showed the strongest associations (threshold 0.16 in the alpha band (a) and threshold 0.11 in the alpha band (b) respectively) Table 3 Predicting social cognition by graph metrics across autistic and non-autistic adolescents EQ Empathy Quotient total score, RMET Reading the Mind in the Eyes Test % correct, AS ToM Animated Shapes accuracy score on the ToM condition. AS Rand Animated Shapes accuracy score on the random condition, R2 partial R2, global efficiency global efficiency in the alpha band threshold 0.22, site UMCU-KLC contrast. The model predicting EQ was not significant (R2 = .10, R2 adjusted = .04; F(7,97) = 1.54, p = .16). With the global efficiency*SRS-2 interaction, the model explained 80% of variance (R2 adjusted =.78; F(9,95) = 42.5, p < .001). The model predicting RMET scores explained 22% of variance (R2 adjusted = .17; F(7, 103) = 4.24, p < .001) and with the global efficiency*SRS-2 interaction included it explained 26% of variance (R2 adjusted = .19; F(9,101) = 3.89, p < .001). The model predicting animated shapes ToM scores explained 17% of variance (R2 adjusted = .12; F(7,99) = 2.99, p < .01), and with the E*SRS interaction included explained 20% of variance (R2 adjusted = .13; F(8,98) = 2.98, p < .005). The control model predicting animated shapes random scores did not reach significance with (R2 = .08, R2 adjusted = .02; F(7,99) = 1.24, p = .29) or without (R2 = .08; R2 adjusted = −.004; F(9,97) = 0.95, p < .48) the interaction EQ (n = 105) RMET (n = 111) AS ToM (n = 107) AS Rand (n = 107) Beta p R2Beta p R2Beta p R2Beta p R2 Global efficiency 224 .16 .03 237 .053 .04 14.22 .44 .01 −0.12 .23 .01 Sex −3.83 .10 .03 −3.12 .17 .02 0.19 .57 < .01 −0.31 .28 .01 Age20.03 .11 .03 0.06 .003* .08 < 0.01 .42 .01 < 0.01 .73 < .01 IQ 0.09 .30 .01 0.21 .007* .07 0.03 .007* .07 < 0.01 .73 < .01 Site 4.71 .17 .03 −8.65 .01* .08 0.3 .57 .06 0.51 .23 .05 Global efficiency*SRS −2.77 .049* .04 0.29 .91 < .01 −0.01 .98 < .01 0.02 .96 < .01 Journal of Autism and Developmental Disorders over-connectivity hypothesis of autism. Developmental Science, 19(4), 524–549. https:// doi. org/ 10. 1111/ desc. 12467 Risi, S., Lord, C., Gotham, K., Corsello, C., Chrysler, C., Szatmari, P., Cook, E. H., Leventhal, B. 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Authors and Affiliations E.deJonge1 · P.Garcés2· A.deBildt1· Y.Groen3· E.J.H.Jones4· L.Mason5· R.J.Holt6· H.Hayward5· D.Murphy5· B.Oakley5· T.Charman7· J.Ahmad8· S.Baron‑Cohen6· M.H.Johnson9,10· T.Banaschewski11· S.Durston12· B.Oranje13· S.Bölte14,15,16· J.Buitelaar17,18· The EU‑AIMS LEAP group· P.J.Hoekstra1· A.Dietrich1 * E. de Jonge [email protected] 1 Department ofChild & Adolescent Psychiatry & Accare Child Study Center, University ofGroningen, University Medical Center Groningen, Lübeckweg 2, 9723HEGroningen, TheNetherlands 2 Roche Pharma Research andEarly Development, Neuroscience andRare Diseases, Roche Innovation Center Basel, Grenzacherstrasse 124, CH-4070Basel, Switzerland Journal of Autism and Developmental Disorders 3 Department ofClinical andDevelopmental Neuropsychology, University ofGroningen, Grote Kruisstraat 2/1, 9712TSGroningen, TheNetherlands 4 Centre forBrain andCognitive Development, Birkbeck, University ofLondon, 32 Torrington Square, LondonWC1E7JL, UK 5 Department ofForensic andNeurodevelopmental Sciences, Institute ofPsychiatry, Psychology andNeuroscience, King’s College London, De Crespigny Park, Denmark Hill, LondonSE58AF, UK 6 Department ofPsychiatry, Autism Research Centre, University ofCambridge, Douglas House, 18B Trumpington Road, CambridgeCB28AH, UK 7 Department ofPsychology, Institute ofPsychiatry, Psychology andNeuroscience, King’s College London, De Crespigny Park, Denmark Hill, LondonSE58AF, UK 8 School ofHuman Sciences, University ofGreenwich, LondonSE109LS, England 9 Centre forBrain & Cognitive Development, University ofLondon, LondonWC1E7HX, England 10 Department ofPsychology, University ofCambridge, CambridgeCB23EB, England 11 Medical Faculty Mannheim, Heidelberg University, Central Institute ofMental Health, Mannheim, Germany 12 Deptartment ofPsychiatry, Brain Center, University Medical Center Utrecht, Utrecht, TheNetherlands 13 Center forNeuropsychiatric Schizophrenia Research (CNSR) andCenter forClinical Intervention andNeuropsychiatric Schizophrenia Research (CINS), Copenhagen University Hospital-Mental Health Services CPH, Glostrup, Denmark 14 Department ofWomen’s andChildren’s Health, Center ofNeurodevelopmental Disorders (KIND), Centre forPsychiatry Research, Karolinska Institutet & Stockholm Health Care Services, Region Stockholm, Stockholm, Sweden 15 Child andAdolescent Psychiatry, Stockholm Health Care Services, Region Stockholm, Stockholm, Sweden 16 Curtin Autism Research Group, Curtin School ofAllied Health, Curtin University, Perth, WA, Australia 17 Department ofCognitive Neuroscience, Donders Institute forBrain Cognition & Behavior, Radboud University Medical Center, Nijmegen, Gelderland, TheNetherlands 18 Karakter Child & Adolescent Psychiatry University Centre, Nijmegen, Gelderland, TheNetherlands