Exploring the social cognition network in young adults with autism spectrum disorder using graph analysis

Abstract Background Autism spectrum disorder (ASD) is characterized by an impairment in social cognition (SC). SC is a cognitive construct that refers to the capacity to process information about social situations. It is a complex network that includes distinct components. Exploring how SC components work together leads to a better understanding of how their interactions promote adequate social functioning. Our main goal was to use a novel statistical method, graph theory, to analyze SC relationships in ASD and Typically Developing (TD) individuals. Methods We applied graph theory to SC measures to verify how the SC components interact and to establish which of them are important within the interacting SC network for TD and ASD groups. Results The results showed that, in the TD group, the SC nodes are connected; their network showed increased betweenness among nodes, especially for the Theory of Mind. By contrast, in the SC network in the ASD group the nodes are highly disconnected, and the efficient connection among the components is absent. Conclusion ASD adults do not show SC competencies and functional communication among these skills. Under this regard, specific components are crucial, suggesting they could represent critical domains for ASD SC.


A fundamental component of SC is the Theory of Mind (ToM):
The ability to attribute mental (cognitive ToM) and emotional (affective ToM) states to oneself and others, and to use these attributions to make sense of and predict behavior (Baron- Cohen et al., 1985;Mazza et al., 2017;Warrier & Baron-Cohen, 2018). We know that during the early months of their lives, individuals with ASD already display impairment of the SC precursors (e.g., emotion processing, sensitivity to ostensive signals, and joint attention, among others (Happé & Frith, 2014;Warrier & Baron-Cohen, 2018)). According to recent literature Pino et al., 2018Pino et al., , 2017, individuals with ASD are characterized by a delay in the development of SC capacities rather than a total lack of these complex domains/constructs. Indeed, in Typically Developing (TD) children, SC capacities emerge in a specific sequence (Happé & Frith, 2014;Pino et al., 2018Pino et al., , 2017. Individuals with ASD are characterized by the same sequence in the development of these competencies; however, the competencies develop later than in TD children . According to Happé and Frith (2014), SC can be understood as a complex network diagram that includes distinct components such as emotion processing, biological motion perception, empathy, ToM, self-processing, affiliation, and social identity. All these components are interrelated, and their typical development promotes appropriate social behavior (Happé et al., 2017;Happé & Frith, 2014).

Nevertheless their work does not explain how components could in-
teract and how components influence each other. Our study is based on the theoretical framework of Happé and Frith (2014) setting up a simplified model of their network, relying on collected data, which represents the relations between components as well as categorizes graphically their intuition of SC. Thus, SC cannot be considered as a single and independent process, but rather is a complex construct in which the different components work together in an as yet unknown way. Along these lines, a study of the SC components working together could lead to a better understanding of the influences they have on each other, an understanding that would not appear if the components were analyzed in isolation.
A method for evaluating interactions of this kind is graph theory.
Indeed, graph theory allows the exploration of associations among interacting elements in a complex network such as the SC domain, the rationale for applying graph theory is that it allows to devise and test structures in terms of components' connections with the associated path properties (Ibrahim et al., 2016). This type of method can be understood as an ecological approach, in which the SC components are connected together to resolve a social situation and to construct an adaptive response; in fact, the interrelation among the SC components is crucial to developing social behavior and maintaining stable social relationships (Happé & Frith, 2014;Mazza et al., 2017;Pino et al., 2018).
In this regard, we suggest that adults with autism, as a result of the delay in the development of SC components , could have a dysfunctional or poor social network in which the SC components fail to work effectively to ensure good social functioning.
In this study, therefore, we applied graph theory to behavioral data to verify how the SC components interact and to establish which SC competencies are important within interacting social networks; the theory was applied to both ASD and TD adults, after which the analysis took place. Four SC measures (Basic Empathy Scale; Eyes Task; Empathy Quotient; Advanced ToM Task) were used in this study to evaluate several aspects of the SC constructs ToM, social behavior, and empathy. Specifically, we used these tests because they provide a complete evaluation of mentalizing and empathic abilities. As regards mentalizing tests, the Eyes Task (Baron- Cohen, Wheelwright, Hill, Raste, & Plumb, 2001) is considered to test the first level of ToM, since it involves the first stage of ToM attribution of the relevant mental state (e.g., compassion) through the observation of the ocular area of face (a visual stimulus). The second stage of ToM attribution involves understanding the content of that mental state (e.g., compassion for a woman who has lost her mother); this is measured by the Advanced ToM Task (Happé, 1994), which evaluates the second stage of ToM through a verbal stimulus. Regarding empathic abilities, the Basic Empathy Scale (Albiero, Matricardi, Speltri, & Toso, 2009;Jolliffe & Farrington, 2006) measures five basic emotions (fear, sadness, anger, and happiness), and the measurements relate more generally to cognitive and affective empathy rather than a specific affective state (e.g., anxiety). The scale is based on the definition of empathy proposed by Cohen and Strayer (1996), as the sharing and understanding of another's emotional state or context resulting from experiencing the emotive state (affective) and understanding the other's (cognitive) emotions. The Empathy Quotient (Baron- Cohen & Wheelwright, 2004) is more complex; in fact, the authors based this scale on a model in which empathy has both affective and cognitive components. However, some evidence suggests that the scale may consist of three factors (Lawrence, Shaw, Baker, Baron-Cohen, & David, 2004;Muncer & Ling, 2006) and thus that it also evaluates social skills ability. The Empathy Quotient, compared to the Basic Empathy Scale, evaluates the capacity to share mental states rather than just emotional states.
Using graph theory, we represented the SC components using nodes and their relationships using edges; we then evaluated how these nodes exchanged information and how this differed between ASD and TD groups. We highlight the fact that the qualitative and topographical network differences between atypical and typical development populations could lead to a better understanding of the relationship between social impairments and symptomatology.

| Participants
Our study included 65 male ASD participants who were selected by the Regional Centre for Autism, Abruzzo Region Health System, L'Aquila, Italy (mean ± standard deviation chronological age = 21.43 ± 2.06), and 61 male TD participants recruited from the University of L'Aquila, Italy (mean ± standard deviation chronological age = 21.52 ± 1.97). No differences between the groups (ASD and TD) emerged for chronological age (F 1,124 = 0.06, p = .80).
The ASD diagnoses were provided by experienced clinicians according to the new criteria of the DSM-5 (American Psychiatric Association, 2013). These diagnoses were confirmed using the Autism Diagnostic Observation Schedule, second edition (Lord et al., 2012) and the Autism Diagnostic Interview-Revised (Rutter, Le Couteur, & Lord, 2003). Given their chronological age, the individuals with ASD and TD were tested with the Wechsler Adult Intelligence Scale (WAIS-IV; Wechsler, 2008; see Table 1).
It was crucial that participants in the TD group had not been diagnosed with any neurological or psychological disorders.
All the participants were tested individually in a quiet room fol- The socio-demographic and clinical information for the two groups of participants is summarized in Table 1.

| Basic empathy scale (BES)
The BES is composed of two subscales: the Affective Empathy Subscale (AES) and the Cognitive Empathy Subscale (CES; Albiero et al., 2009;Jolliffe & Farrington, 2006). The AES is composed of 11 items that measure an individual's ability to share another person's emotions.
An example of the type of item in the AES is: "My friend's emotions don't affect me much." The CES comprises nine items and measures the person's understanding of another person's emotions (Jolliffe & Farrington, 2006). Examples of items in the CES are: "I can understand my friend's happiness when she/he performs well in something," and "When someone is feeling down, I can usually understand how they feel." The participants had to give their ratings on a five-point Likerttype scale ranging from 1 = strongly disagree to 5 = strongly agree.
The scores for each item were summed, giving a total score for each subscale (AES and CES) which we used in our analysis.

| Eyes task (ET)
The Eyes Task is a revised version of the "Reading the Mind in the Eyes Test"; this test was considered by Baron-Cohen et al. (2001) to be a first level ToM test. The respondents are given 36 photographs depicting the ocular area of an equal number of different actors and actresses. In the corner of every photograph, four emotional descriptors (e.g., dispirited, bored, playful, or comforting) are printed, only one of which (the target word) correctly identifies the depicted person's mental state, while the others are included as foils. The overall score totals the number of items (photographs) for which the participant correctly identifies the emotional descriptor. The maximum total score is therefore 36. The total score for the Eyes Task was used in our analysis.

| Empathy quotient (EQ)
The EQ is a self-reported measure evaluating different aspects of empathy, using cognitive, social skills, and emotional subscales (Baron- Cohen & Wheelwright, 2004 TA B L E 1 Demographic data for ASD and TD groups and clinical information concerning the ASD group is evaluated by three subscales of the EQ: cognitive empathy (CEQ) and social skills (SSQ), which measure, respectively, the capacity to understand the perspective of the other person, and a number of regulatory mechanisms that keep track of the origins of one's own and others' feelings. The emotional dimension is evaluated by the emotional subscale (EEQ). An example of the items is "I find it hard to understand how to behave in a social situation." Each answer can vary from 0 (strongly agree) to 4 (strongly disagree). An algorithm permits the responses to be coded according to the response and the item to which it refers, each response in 0, 1, or 2 scores. The item scores are then summed according to their subscales (CEQ, SSQ, and EEQ). The total scores for each subscale were used in our analysis.

| Advanced theory of mind task (A-ToM)
The A-ToM is an Italian adaptation of a cognitive task that Blair and Cipolotti (2000) used and that was first proposed by Happé (1994 Speech, Appearance/Reality, Forgetting, Irony, and Persuasion. The subject obtains a score ranging from 0 to 1 for each question. A total score, in the range 0-13, is then obtained by summing the scores obtained for each item. We used this total score in our analysis. Happé (1994) used the term "advanced" to refer to a story that contains the comprehension question, where the key questions in the task concern a character's mental state (the experimental condition).

| Standard analysis
We performed ANOVA for between-group comparisons, and the results were adjusted using Bonferroni's correction. The analyses were performed using R (R Development Core Team, 2008).

| Network analysis
Graphs give a better way of dealing with abstract concepts like relationships and interactions, and they also provide an intuitive visual way of thinking about these concepts (Kellermann, Bonilha, Lin, & Hermann, 2015;Shirinivas, Vetrivel, & Elango, 2010). According to Ibrahim et al. (2016), the concepts of graph theory make a good method for the analysis of complex networks. In the present study, we used the graph analysis to define the relationships between social cognition domains. In graph theory, the variables are termed "nodes" and they are connected via "edges." Edges can be weighted, and an edge with a higher weight is more strongly connected with a node than an edge with a lower weight. Moreover, edges can be directed, meaning that the edge between nodes A and B is different from the edge between nodes B and A (Opsahl, Agneessens, & Skvoretz, 2010

| Network analysis: construction of the network
Two graphs were constructed, one for the ASD group and one for the TD group, with the nodes representing psychological domains (in our study, the nodes represented SC components/abilities) obtained from the assessed tests. We transformed all the scores for the SC measures into z-scores to allow a better comparison of the data. Networks were then estimated using the Gaussian graphical model (Lauritzen, 1996), in which edges can be directly interpreted as partial correlation coefficients using the covariance matrix as the input. This task was carried out using the command estimate network (Epskamp, Borsboom, & Fried, 2018) provided by the bootnet package running in the R software. Only significant partial correlations were maintained, in order to maintain only important edges.
After the construction of the graph, we evaluated some canonical centrality indices, such as the strength, betweenness, and closeness of each node (i.e., each SC component) (Epskamp et al., 2018).
Specifically, strength represents a weighted measure of the degree between a node and any other node connected to it. It is given by the formula: where k represents the strength, and w represents the weight between the nodes i and j. We decided to set w ij as the correlation coefficient between the nodes i and j. This form of local connectivity defines how much this construct is able to correlate (communicate) with the adjacent nodes.
The need to model the capacity of a node to link to other nodes has been defined using the concept of betweenness, which represents how many times a node is important in the average path between two other nodes: where p jk represents the number of shortest paths between nodes j and k, and p jk (i) is the number of shortest paths between nodes j and k that pass through node i. A node with higher betweenness has a higher number of shortest paths that pass through it.
Closeness represents the average length of the shortest path between the node and any other node: where d represents the length of the shortest path between node j and i, and n represents the number of nodes. Closeness can be considered to be a measure of how long it takes for a piece of information from one node to reach other nodes. This definition characterizes the strength of the connectivity with all the network nodes, not just the nearest ones. A lower value of this measure represents a lower distance from the node to others, and thus, closeness indicates how central a node is.

| Network analysis: groups comparison
In order to evaluate the differences between the TD and ASD networks, we bootstrapped each network 1,000 times, and for each bootstrap, we obtained the strength, betweenness, and closeness for each node. This computation was performed using the bootnet command, selecting the replacement option. Statistically significant differences between the measures were then evaluated using the z test and were adjusted by Bonferroni's correction (α = 0.05).
For the analysis, we used the bootnet package (Epskamp et al.,

2018) from the R statistical analysis tool (R Development Core
Team, 2008).

| Ethics approval
Written informed consent was obtained from participants according to the Declaration of Helsinki, and a local ethics committee approved the study.

| ANOVA
TA B L E 2 Significant differences between groups (ASD and TD) for social cognition measures and canonical properties of graph analysis (betweenness, closeness, and strength) for each node (i.e., social cognition components)

Social cognition measures
Measures score mean(SD)  (F 1,124 = 135.09; p < .01) compared to the TD group. The results of these analyses are reported in Table 2.

| Visualization of the networks
The networks are represented in Figure 1. The nodes represent the different SC components. The lines between the nodes represent the correlations between the measures. The width of the lines indicates how strong a correlation is, while red and blue lines represent positive (blue) and negative (red) correlations. Closeness is represented by the node's distance.

| Graph measures
In Figure 2, the centrality indices (strength, betweenness, and closeness) of each node (SC components) for each group (ASD and TD) resulting from the original sample and from the bootstrap are reported. The graph analysis on the centrality indices of each node and between groups showed significant differences between the nodes of the ASD and TD graphs in strength and betweenness properties. No significant differences were found for the closeness property (see Table 2). Specifically, the TD group showed higher betweenness for the SSQ of EQ node (z = 4.43, p < .01), and higher betweenness for the A-ToM node (z = 6.12, p < .01), compared to the ASD group. Moreover, the TD group had higher strength for the ET node (z = 6.84, p < .01), the SSQ of EQ node (z = 6.36, p < .01), and the A-ToM node (z = 9.53, p < .01), compared to the ASD group.

F I G U R E 1 Graphs of ASD and TD populations. Each node represents a SC domain. Strength is represented by the edge's thickness and
By contrast, for the CES of BES node, the ASD group showed higher strength (z = −3.30, p = .02) compared to the TD group.
It is interesting to note that the betweenness for the AES of BES node showed a substantial trend toward being statistically significant, with the ASD group showing higher betweenness (z = −3.04, p = .05) than the TD group.
The graphs for the ASD and TD groups are reported in Figure 1, and the values of the betweenness, strength, and closeness properties are reported in Table 2.

| D ISCUSS I ON
The aim of this study was to explore the domain of the SC network in young adults with autism, compared with TD adults as a control group, using graph theory. We built two separate networks of SC components, one for ASD and one for TD, in order to map the interacting associations among the components that characterize this construct.
Indeed, the SC construct can be defined as a complex network in which interacting components, such as ToM, emotion processing, empathy, self-processing, and social identity, influence each other (Happé & Frith, 2014;Warrier & Baron-Cohen, 2018). Individuals with ASD are characterized by a delay in the development of SC competencies Pino et al., 2018Pino et al., , 2017. In this regard, we highlight the fact that it is important to evaluate the SC network to determine the relationship among the SC domains and, at the same time, to verify the efficiency of interacting SC networks in young adults with autism to understand how this affects their general social functioning. Therefore, we have outlined, using graph theory, the profile of the SC domain for both typical and atypical populations (TD and ASD groups, respectively).
First, we showed that our individuals with ASD show differences in the SC measures (Eyes Task, BES, EQ, and A-ToM Task) used in this study, compared to TD individuals. This result is in line with the more recent literature Warrier & Baron-Cohen, 2018), and it confirms that SC difficulties are a central feature in ASD individuals. For this reason, it has become important to understand how these abilities interact. Graph analysis seemed to be a useful type of statistical analysis for studying the interaction among several of the SC abilities.
Our graph analysis results showed that the SC network is significantly different in the TD and ASD groups. It must be pointed out that our results must be interpreted with some caution, as our analysis describes connectivity between SC domains without specifying how a node processes the information or the direction of the information flow that follows. The first result was that in the TD group all the SC nodes are connected, while in the ASD group the dimensions are highly disconnected (see Figure 1). shows that the network works as a single component, social cognition (see Figure 1). An isolated SC network does not mean impaired node processes, but it means that the components do not relate to each other during a social situation. This isolation could be con- ing to lead to the correct interpretation (a fake smile). This could be true even when there are more social clues that complement a correct understanding. Indeed, the SC network of the TD group showed increased betweenness among nodes, specifically the A-ToM (the complex cognitive capacity) and the SSQ of EQ (social skills abilities) nodes, compared to the ASD group. This finding suggests that these processes represent important hubs of connection that differentiate between ASD and TD individuals when a social situation occurs. Specifically, A-ToM represents the capacity to understand the perspective of another person, while SSQ of EQ represents a mechanism that keeps track of the origin of one's own and another's feelings. As betweenness represents how paths pass through that node, it is conceivable that these paths support the connection between the cognitive and affective dimensions of empathy (EEQ of EQ and AES of BES) in the network (see Figure 1), allowing information to spread through multiple nodes, although the nature of the support (e.g., monitoring or integrating information) cannot be demonstrated.
Indeed, the TD individuals showed greater strength in the A-ToM, ET, and SSQ of EQ measures, compared to the ASD group.
These results underline the importance of the influence of A-ToM and SSQ of EQ in the network in combination with ET, suggesting that their information has a major local influence on the TD network compared to the ASD network. Future research should be directed toward understanding how node processes effectively contribute to the network (e.g., by integrating or controlling information) and how edges change over time.
It is plausible that these structures are time-dependent, especially during early development, and it would be interesting to understand when the structure of SC becomes permanent. It would be also interesting to know the level at which the SC network structure can be changed-whether it can be changed topologically or in the magnitude of its edges. Hypothetically, an intervention could try to work on the strength of the edges to improve the network connections, although the poor connectivity in ASD may suggest that intervention in relation to a single component would not be enough to give an important improvement when ASD individuals are facing social situations, because it is possible that any improvements would not influence the SC domain, although future studies should investigate this point.

| CON CLUS ION
ASD domains of SC network result isolated compared to TD which results connected, so that the number of connected components changes from one in the TD group into scattered isolated or low connected components in the ASD group. The model obtained from the TD network fits the theoretical SC network model proposed by Happé and Frith (2014), where components are connected to each other. Network indices comparison between TD and ASD group show a different communication role and statistical weight of the SC network nodes. These differences deserve a better understanding and evidence because they could provide strategical indication to impact ASD social functioning as well as their social isolation.

CO N FLI C T O F I NTE R E S T
The authors declare that they have no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
The datasets generated and/or analyzed during the current study are not publicly available, because the data were obtained in the course of mental health care, but they are available from the corresponding author on reasonable request.