Disturbances in speech have been recognized as a key component of both positive and negative symptoms in psychosis1. Here we define speech as the sum of all acoustic and lexical aspects of spoken communication. Increasingly, speech phenotypes in psychosis can be objectively and reliably measured through automated language analysis for the detection and prediction of psychotic disorders2,3,4,5,6,7. Speech graphs, derived from transcribed texts, have shown the ability to accurately quantify language disorganization and impoverishment. There were significant relationships between graph features and key psychosis phenotypes, including thought disorder, cognition, global functioning, and brain connectivity changes8. Speech graphs are network representations of discourse that treat linguistic elements (words, lexemes, etc.) as nodes and relationships among those elements as the bridging links (edges)9. Generally, relationships among linguistic elements may be structural (based on the relative locations of the words, e.g., occurring in sequence or co-occurrence in the same utterance) or semantic (based on the meaning of the utterance, e.g., entity A is acting upon entity B). Quantitative measures of the size, connectedness, and organizational structure of the speech graphs can then be calculated10. For example, the size of the graph can be quantified by the number of nodes and edges as well as measures of internal distances such as network diameter and average shortest path length. The connectedness of the graph is reflected in average degrees, graph density, and size of the largest connected component. The degree of organization in the graph can be measured by comparing the statistical similarity of graph features to randomly generated graphs of the same size.

Sequential speech graphs of individuals with psychosis spectrum disorders (PS+) have been characterized as being smaller, less connected, and more disorganized than individuals without psychosis spectrum disorders (PS−). In their pioneering study, Mota and colleagues showed that the PS+ speech graphs exhibited fewer nodes and edges, lower average degrees, and smaller connected components compared to those of healthy controls and patients with mania11. PS+ speech graphs also had a lower average shortest path length and network diameter per fixed word lengths, reflecting shorter internal distances12. A subsequent study comparing the size of connected components in speech graphs with that of randomly generated graphs of the same size revealed that PS+ graphs have more random-like organization compared to PS−13. Palaniyappan et al.8 further showed that the graph measures of connectedness (size of connected component) and organization (size of the connected component divided by that of random graphs) were associated with disorganized and impoverished thought disorders as well as clinical measures of schizophrenic symptoms and biological measures of neural connectivity.

However, sequential relationships among words are vulnerable to non-psychopathologic factors such as stylistic preferences of the speaker, passive or active voice, and different grammatical structures in different languages. On the other hand, semantic relationships are tied to the underlying concepts being expressed, and they are consistent across languages and speaking style. For instance, in “The dog chased the cat” and “The cat was chased by the dog,” the same semantic content is expressed with different word sequences. Furthermore, there is evidence that thought disorder is related to disruptions in semantic networks14. Thus, graphs that utilize the core semantic content may be a more direct method for representing disrupted brain circuits in psychosis. Here, we attempt to build speech graphs upon two semantic relations which have been proposed as universal linguistic relationships15: (1) Action, which links the actor of the underlying event to its undergoers (dog → cat), and (2) predications, which link the predicate of the utterance to its arguments (chase → dog and cat). These relationships capture the core semantic meaning of the utterance: who does what to whom? Figure 1a illustrates the structures of sequential and action-predication graphs.

Fig. 1: Speech graph methodology.
figure 1

a Structural and semantic graph representations of a given text are illustrated. The structural representation is produced based on sequential relations between lemmatized content words (e.g., I→see→cookie→jar, etc.). The semantic representation is produced by connecting elements that act upon each other (e.g., I→chair; kid→cookie jar), and linking verb predicates to their arguments (e.g., see→I; see→chair; grab→kid; grab→cookie jar). b Dynamic graph features are computed by sliding a window of fixed length throughout each sample to produce n instances of graph representations. Subsequently, each graph feature is calculated as the mean value of n features each belonging to a particular instance. Successive sequential graphs progress one word at a time in windows of 30 words, and semantic graphs slide one utterance at a time in windows of three utterances.

In this paper, we aim at (1) introducing a new way to produce semantic speech graphs based on the two universal linguistic relations of action and predication, (2) verifying the validity of size, connectedness, and organization as three non-redundant domains of speech graph features, (3) comparing semantic and structural graph measures of size, connectedness and organization in their associations with the presence of psychosis, and (4) examining the relationship between graph features and clinically rated dimensions of psychosis symptoms. The overall goal is to operationalize semantic speech graph methodology with respect to studying language disturbance in psychosis and guide subsequent studies.


Participant characteristics

In total, speech samples of 205 and 201 participants were collected and transcribed for picture description and open-ended narrative tasks respectively, corresponding to 81 PS+ and 124 PS− participants (Table 1). On average, picture descriptions included 110 ± 66 words and narrative responses included 162 ± 121 words; word counts were not significantly different between PS+ and PS− (p-values were 0.310 and 0.051 for open-ended narrative and picture description tasks respectively). As expected, PS+ participants scored significantly higher in overall psychosis symptoms, negative symptoms, and demonstrated significantly more abnormal speech per clinical ratings.

Table 1 Demographic characteristics of the participants.

Speech graphs formation and measurements

The structural graphs were formed by the sequential connection of elements of structural graph entry irrespective of utterance boundaries. The semantic graph representations were created by first tagging verbs, actor-arguments and undergoer-arguments using semantic role labeling, and then combining action relations (actor → undergoer) and predication relations (verb-predicate → actor and undergoer arguments) within each utterance (Fig. 1a). Iterations of the same relationships were captured as the edge weight; the first occurrence was weighted 1 and repetitions added 1 to the edge weight incrementally. The performance of the semantic role labeler was inspected and did not appear to demonstrate any biases (Supplementary Table 2). The code for the formation of semantic graphs is shared in a public repository ( A more comprehensive illustration of the applied method is presented in Supplementary Table 2.

  • Utterance Example: The kid is grabbing the cookie jar.

  • Structural Graph Connections: kid → grab + grab → cookie + cookie → jar

  • Semantic Graph Connections: grab → kid + grab → cookie jar + kid → cookie jar

Size, connectedness, and organization of sequential and action-predication networks were measured by computing relevant graph features. Graph size was quantified with straightforward counts (number of nodes (NN), number of edges (NE)) and internal-distance measures (diameter, average shortest path length between any two nodes (ASPL)). Connectedness was quantified using average weighted degree (i.e., the number of weighted edges for each node; AWD), graph density (realized edges divided by possible edges) and number of nodes in the largest strongly connected component (LSCC). The level of organization in graphs was estimated by computing the z-score of ASPL and LSCC relative to 1000 randomly generated graphs of the same NN and NE. All calculations were performed in Python using the igraph library16. Random graphs were generated using the built-in Erdős–Rényi algorithm17.

Static graph features were calculated based on the networks of the whole response for each task, and averaged across each task category for each participant (picture description vs. narrative). We complemented usual static graph features with moving-window measures introduced by Mota and colleagues12. The length and moving-step of the window were set to 30-tokens length and 1-token step for the sequential graphs based on the best performing models in previous studies which explored this technique8,12,13. Action-predication networks were calculated for 3-utterance segments and 1-utterance steps because these lengths were the closest equivalents to that of structural graphs, considering the mean sentence length of ~10 words. Dynamic graph features were then calculated as the average of graph features over all windows. In total, 36 graph features (n = 18 for structural graphs, n = 18 for semantic graphs) were analyzed. The full list of graph features is included in Supplementary Table 3. Graph formations and measurements were performed separately for each response (i.e., each picture or open-ended prompt) and then averaged across the task for each participant.

The redundancy of graph features

To evaluate the mutual redundancy of different sets of graph features, we computed variance inflation factors (VIF) at successive layers of analysis18: first, across domains (size, connectedness, and organization), then across modes (static and dynamic), then for each type of graph (structural and semantic), and finally for each task category—picture description (Table 2) and open-ended narratives (Supplementary Table 4).

Table 2 Survived graph features in sequential VIF comparisons in picture description task.

Intra-domain VIF analyses revealed that the information in the internal-distance measures was not redundant with respect to general measures of size. All connectedness measures in both graph types survived in the intra-domain analysis. Dynamic organization measures of sequential graphs were not mutually redundant, but only one of the dynamic organization measures survived in the VIF comparison of the action-predication networks. Increasing the level of integration did not lead to exclusion of one entire domain. Notably, dynamic semantic graph features of all three domains of size, connectedness, and organization remained in the final sets in both tasks; this was not observed in other types of graph features.

Speech graph features and psychosis

Associations between graph features and the presence of psychosis are presented in Table 3. In general, semantic graphs showed a more task-specific behavior compared to structural graphs, with more significant associations in picture descriptions. Structural graphs performed similarly in picture description compared to open-ended narrative tasks. The moving window method enhanced the significance and effect size of the relationships for both graph types and for all three domains of size, connectedness, and organization. In order to account for the uneven distributions of sex and race in PS+ and PS−, we selected two subsamples of participants matched for sex and race, respectively. The correlations between graph measures and psychosis status were consistent with the overall findings in each matched subsample (Supplementary Table 5).

Table 3 Relationships between structural and semantic graph features and psychosis.


Speech from PS+ yielded significantly smaller structural and semantic graphs as reflected in multiple correlations between measures of network size and psychosis (Table 3-A). The moving-window technique improved the correlations in both graph types with ~0.1 increase in mean RBC for sequential and action-predication graphs respectively. General measures of the network size (NE and NN) manifested the strongest and most significant correlations in psychosis for both graph types and in both tasks.


Psychosis was associated with smaller connected components and higher graph densities (Table 3-B). This pattern was observed in both structural and semantic graphs. However, average weighted degrees were higher in the structural graphs of psychotic speech and lower in semantic networks compared to non-psychotic counterparts. The most informative semantic graph features in this domain were dynamic graph density and LSCC for open-ended and picture description tasks respectively. Dynamic density in sequential graphs showed the highest effect size in both tasks (picture description: p < 0.001, RBC = −0.33; narrative: p < 0.001, RBC = −0.31).


Structural and semantic speech graphs showed different patterns of organization with respect to random graphs with negative mean z-scores in semantic graphs and positive z-scores for structural graphs. This pattern was consistent for both measures (LCCZ and ASPLZ) and in both tasks. These findings suggest that action-predication graphs of speech are organized in smaller connected components with shorter inter-nodal pathways compared to random graphs of the same size. Conversely, sequential graphs produce larger connected components with nodes that were further apart. However, in both cases, PS+ graphs incline toward the more random-like patterns of organizations compared to those of PS−, i.e., exhibiting higher z-scores in semantic graphs and lower z-scores in structural graphs (Table 3-C).

Speech graphs and dimensional clinical characteristics

Figure 2a represents task-wise correlation plots for structural and semantic graph features vs. clinical measures of language disturbance (TLC speech disorganization and speech poverty factors), disease severity (BPRS total score) and psychopathological dimensions (BPRS anxiety/depression, hostility/suspiciousness, thought disturbance and withdrawal/psychomotor retardation factors; SANS affective flattening, alogia, avolition, and asociality/anhedonia global scores). In general, graph features generated from the picture description tasks were more closely related to clinical measures than those from narrative tasks. Within the picture description task, the dynamic action-predication graph features outperformed the static features as well as both static and dynamic sequential graph features (Fig. 2a). Among graph measures of the narrative task, a dynamic measure of structural graph organization (D_SEQ LSCCZ) showed the strongest connections with clinical characteristics.

Fig. 2: Correlations between structural and semantic graph features and dimensional clinical characteristics.
figure 2

a Heatmap representations of the Spearman’s correlation coefficient for structural and semantic graph features and clinical measures in picture description and open-ended narrative tasks across all participants. Significant relationships with uncorrected p values < 0.05 are shaded based on their effect sizes (Spearman’s rho). Correlations surviving Bonferroni correction are starred. Bar plots of correlation coefficients per clinical dimension are available in Supplementary Fig. 2. b Network representation of significant relationships between graph features and clinical measures. Multi-collinearities were separately handled for structural and semantic graph features by stepwise comparison of variance inflation factors and feature exclusion. Multiple comparisons were accounted for using Bonferroni correction. S_AP static action-predication graph feature, D_AP dynamic action-predication graph feature, S_SEQ static sequential graph feature, D_SEQ dynamic sequential graph feature, NN number of nodes, NE number of edges, diameter graph diameter, ASPL average shortest path length, AWD average weighted degree, density graph density, LSCC size of largest strongly connected component, LSCCZ z-score of LSCC compared to 1000 random graphs, ASPLZ z-score of ASPL compared to 1000 random graphs. More details on graph features are available in Supplementary Table 3.

Clinical measures of speech disturbance

Speech disorganization was associated with increased connectedness and decreased organization in both tasks. This relationship is more prominent in structural features with more Bonferroni survived correlations and higher correlation coefficients (absolute rho = 0.36–0.39). Speech poverty was correlated with the density and size of graphs of both type, with impoverished speech having denser and smaller graphs; this correlation was more clearly observed in the semantic networks than in the structural graphs (absolute rho = 0.40–0.41).

Overall disease severity

The strongest correlates of total BPRS score were dynamic measures of size (rho = −0.54 to −0.58) and organization (rho = 0.51–0.54) of semantic graphs in the picture description task. For narratives, the same relationships were reproduced, but there was a stronger correlation between overall disease severity (BPRS total score) and the dynamic organization measure (LSCCZ) of structural graphs (rho = −0.45).

Dimensional measures of psychosis

Figure 2b shows the significant relationships among non-redundant graph features and clinical measures. Patterns were task-dependent. Semantic graph features derived from picture description tasks were consistently more informative for dimensional measures of psychosis than structural features. Multiple connections were observed between semantic graph features from picture description and multiple psychopathological dimensions including hostility/suspiciousness, thought disturbance, withdrawal/psychomotor retardation, affective flattening, and avolition. Thought disturbance was strongly correlated with almost all dynamic graph features in the Action-Predication network (rho = −0.4 to −0.62). Negative factors of withdrawal/psychomotor retardation and affect flattening were connected to static and dynamic measures of connectedness in semantic graphs. Dynamic measure of structural graph organization (LCCZ) was connected with multiple clinical dimensions in open-ended narrative task, including avolition, thought disturbance, and hostility/suspiciousness (absolute rho = 0.4–0.45). The only domain that remained uncorrelated in both tasks for all graph features was the anxiety/depression factor.


Here, we presented an automated speech analysis method that objectively measured speech quantity, connectedness, and organization using graph metrics. These features were quantitative and objective, and they captured semantic relationships of action (between actors and undergoers of utterance) and predication (between the predicate and arguments).

We found that the semantic graph features derived from the picture description tasks were strongly correlated with psychopathological dimensions of psychosis, with the dynamic features outperforming the static features. Our findings suggest that incorporating semantic information in graph modeling of speech can increase the performance of such models. In the picture description tasks, only the semantic graph features were connected to psychopathological dimensions other than language disturbances, including dimensions such as affect, abolition, and thought content. There are no other existing reports of the use of semantic graph methodology in studying psychosis. Therefore, this finding remains to be replicated.

Speech graphs of PS+ were smaller, less connected, and more randomly organized compared to those of PS−. This was true for both semantic and structural graphs in our study, and the finding is consistent with previous studies using structural speech graphs11,12,13. For example, Mota et al. found that schizophrenia was related to decreased size in terms of the number of nodes11 and measures of internal distances12. The association between psychosis and decreased speech graph size may reflect a similar phenomenon as the decreased semantic density found by Rezaii et al.5 and decreased idea density reported by Moe et al.19. With regard to measures of connectedness and organization, recent studies have relied on the LSCC, the largest strongly connected component, as an absolute and relative quantity with respect to randomly generated graphs8,20,21. Our findings suggest that additional information can be captured with other non-redundant features describing size, connectedness, and organization. For example, we found that diameter and average short path length convey non-redundant information about the expansiveness of the network in addition to number of nodes and edges, network density and average degree can be used along the connectedness measure of LSCC, and z-score analysis of ASPL can be considered as a measure of speech graph organization. Each of these graph metric domains should be included in future efforts to quantify clinical speech characteristics.

We found that graph features are related to psychosis in a task-dependent manner. Previous studies reported that dream reports and picture description tasks are more informative about psychosis compared to narrations pertaining to everyday life, as reflected in larger effect sizes for association with psychosis12,13. Since not all participants are able to recall and report dreams13, picture descriptions have developed into the preferred source of speech samples for graph analysis8,20. Accordingly, our findings suggest better performance of speech graphs based on picture description tasks compared to open-ended narratives. It may be the case that the additional structure provided in these tasks is able to reduce noise—i.e., variations in speech that are not related to psychopathology, which may be more dependent on the mood or social status of individual speakers. Furthermore, relative to open-ended narratives, picture description tasks have a pre-set common ground between speaker and listener: the picture. This setting helps navigate the speaker’s response, making it relevant and informative enough for graph analysis. Although everyday verbal communications are not directed by specific tasks, picture descriptions seem suitable for brief speech sampling for computational language analysis in clinical context. Further studies with larger open-ended narrative speech samples may show similar results.

Moreover, we found that controlling the amount of speech using the moving-window method enhanced the performance of speech graph models. This is in line with previous studies conducted by structural speech graphs, where different approaches attempted to control speech quantity, including using normalized features (i.e., measuring features per word count)11, setting time limits for speech recordings8,13,20, and incorporating moving-window methods (i.e., using dynamic graph features)8,12,13. Mota and colleagues reported that measuring graph features per word count reversed the relationship of graph features with psychopathological conditions (e.g., the number of nodes were lower in the speech graph of patients with schizophrenia compared to that of patients with manic disorder, but this was reversed when normalized for word count)11. Therefore, to make the methodology more uniform and applicable to a variety of samples, we suggest using dynamic graph features for subsequent studies.

There are several limitations to the current study. The scope of our comparisons was focused on psychosis as a heterogeneous and multi-faceted condition. Future studies should evaluate whether there are more fine-grained relationships between semantic graph features and psychosis subtypes, as well as whether the presence of potentially comorbid conditions, differences in treatment history, and social determinants affect these measures. In addition, participants of our study were recruited from both inpatient and outpatient services and included individuals with and without formal thought disorders. This heterogeneity might have contributed to our dimensional characterization of clinical symptoms. Future studies should evaluate the clinical correlates of semantic graph features in specific subpopulations, for example in early psychosis, acute hospitalization, chronic psychosis, and other groups. Sampling methods were not uniform across the entire sample, as further detailed in the method and supplement. Our primary findings remained consistent when accounting for these deviations statistically. Although we utilized lemmatization of words to merge different inflected forms of lexical units, shared entities that are addressed by different words stayed detached from each other. Incorporating an algorithm to identify co-referents can help better represent the semantic structure of discourse. Moreover, devising more sophisticated methods sensitive to the different senses of each word will be able to enhance the performance of similar models in future studies. We have limited our semantic model to the relations between actors and undergoers. However, semantic theories have identified a variety of more differentiated semantic roles such as experiencer, instrument, source, and goal that can be used to produce more fine-grained semantic representations of speech.

The ultimate goal of computational speech measures in the context of psychosis is to develop scalable quantitative methods that improve our understanding of the psychosis disease process and improve our ability to deliver the right treatment to the right person at the right time. The development of novel and informative computational methods moves the field closer to these goals. Our work suggests that graphical speech measures based on semantic relationships capture unique and clinically meaningful aspects of psychosis-related speech disturbances. This method was particularly informative when combined with a moving-windows technique and semi-structured tasks. Future efforts may further refine the semantic graph approach by incorporating more differentiated semantic categories for comprehensive characterization of speech in psychosis spectrum disorders and by relating these features to clinical outcomes like relapse risk and treatment response.


Data acquisition and clinical assessment

Participants (N = 205) were recruited from the Zucker Hillside Hospital inpatient and outpatient services; healthy volunteers were recruited based on prior participation in other studies or through online advertisements. Primary diagnoses of psychotic disorders were established among 81 individuals (36 schizophrenia, 10 schizoaffective disorder, 5 schizophreniform disorder, 18 unspecified psychotic disorder, and 12 mood disorders with psychotic features). 87 had primary diagnoses of non-psychotic conditions, and 37 were healthy volunteers. We were interested in the main effect of psychosis, and so chose to compare PS+ (including schizophrenia spectrum and mood disorders with psychotic features) with PS− participants (healthy volunteers and individuals with non-psychotic disorders). All procedures were approved by the Institutional Review Board and all participants provided informed consent or assent as minors. Each participant provided speech samples in response to three picture description tasks and two open-ended narrative prompts. Open-ended narrative prompts included “Tell me about yourself.”, “How have things been going recently?”, and “How have you spent your time recently?”. For picture description tasks, subjects were prompted to describe scenes with multiple interacting characters and abstract ink blots, as detailed in Supplementary Table 1. Participants were encouraged to talk for at least one minute, but no time limit was imposed on them. The speech samples were collected via three sampling protocols with different ascertainment goals and minor differences in procedures, as detailed in Supplementary Table 1. All assessments and rating scales were completed by the same team of trained research coordinators (SB, LB). Statistically accounting for the protocol differences did not change our primary findings. Additional details on participants and methods are provided in the Supplement.

Clinical measures included the Scale for Assessment of Thought, Language, and communication (TLC) for speech and language disturbances22, the Scale for Assessment of Negative Symptoms (SANS)23, and the Brief Psychiatric Rating Scale (BPRS) for overall psychosis symptoms24. Two-factor scores were calculated from the TLC based on the factor model by Peralta et al. speech disorganization (pressure of speech, tangentiality, derailment, incoherence, illogicality, circumstantiality, and loss of goal) and speech poverty (poverty of speech and poverty of content)25,26. Global scores were taken from the SANS for affective flattening, alogia, avolition, and asociality/anhedonia domains of negative symptoms. BPRS total scores were used as a measure for general psychopathology, in addition to its four factors describing anxiety/depression, hostility/suspiciousness, thought disturbance and withdrawal/psychomotor retardation24.

Language pre-processing

Utterance boundaries were determined manually based on syntactic completeness and the presence of pauses. Within each utterance, tokens were identified by NLTK word-tokenizer27. Each token was tagged for its part-of-speech (POS) and lemmatized using spaCy modules28. Semantic role labeling (SRL) was performed using transformer-srl (, a BERT-based model built as an extension to AllenNLP and pre-trained on CoNLL 2012 dataset derived from the OntoNotes v5.0 corpus29,30,31,32. Semantic roles in OntoNotes are span-based and follow the PropBank formalism where a predicate is annotated with predicate specific, core, or numbered, arguments such as A0, A1, etc., and adjunct arguments such AM-TMP (temporal), AM-LOC (location), etc., which are shared across all predicates. Although core arguments are predicate specific, A0 typically marks the Proto-agent and A1 (and sometimes A2) mark the Proto-patient. For this study we only used a subset of core arguments: A0, A1 and A2, where the relationships between verbs and their arguments captured the predication relationships, and the relationships between A0 and A1 or A2 captured the action relationships33.

For structural graphs, we included nouns, pronouns, non-auxiliary verbs, adjectives, and adverbs. Interjections, filled pauses, articles, and conjunctions (e.g., “yes”, “um”, and “then”) were excluded so as to capture tokens that contribute to verbal exchanges. The lemmatized forms of the included tokens were passed to the graph formation step. We chose to lemmatize the tokens to avoid dissociation of different morphological forms of the same lexeme in network representations (e.g., “talk”, “talked”, and “talking” all merged into the same node labeled as “talk”). For action-predication graphs we tagged verbs, actor-arguments, and undergoer-arguments using SRL, and the lemmatized forms of them were passed to the graph formation step further detailed in the Results section.

Statistical analysis

The associations between graph features and psychosis diagnosis as a dichotomous variable were evaluated using the Mann–Whitney U test. Rank biserial correlation coefficients (RBC) were used as measures of effect size34 and the significance level was adjusted for multiple comparisons by Bonferroni correction (adjusted α = 0.0003). Graph features were correlated with dimensional clinical measures using Spearman’s rank-order test. The significance threshold was adjusted by Bonferroni correction (adjusted α = 0.0001). The correlations between graph feature corresponding to each task and clinical measures were plotted as a heatmap.

Variance inflation factor (VIF) comparison was used to identify redundant graph features in order to simplify our analysis and generate a more streamlined set of features for future applications. First, we applied the method to different features within each domain (size, connectedness, and organization) for static and dynamic types separately. Features with the highest VIF were removed successively until all features showed the VIF of <518. The remaining static and dynamic graph features were integrated for each graph type and the same analyses were conducted. These remaining graph features for structural and semantic graphs were then combined to produce non-redundant graph feature sets for each graph type. A final set of graph features were attained by merging all previously survived features and re-doing VIF analysis over them. The significant relationships between the ultimately survived features and clinical measures were demonstrated as a network for each task.

The potentially confounding effect of different sampling protocols on our results was evaluated by covarying for protocol type in multiple linear regressions predicting clinical measures with graph features of interest (survived VIF and Bonferroni tests). All initial findings remained significant.

All statistical analyses and visualizations were done in python using the Pandas35, NumPy36, Pingouin37, SciPy38, Statsmodels39, Seaborn40, igraph16, and Matplotlib41 libraries.