Abstract
This study, grounded in Cognitive Linguistics and Cognitive Lexical Semantics, uses a graph-theoretical approach to analyze the semantic network of high-frequency Persian verbs as understood by non-native learners. It builds on 50 foundational Persian verbs from Jamshidi et al. (2022) and involves 101 non-native Persian speakers from Imam Khomeini International University. Participants, whose native language is not Persian, used a culturally adapted version of Schur’s (2007) semantic association questionnaire to graphically represent perceived semantic relationships among the verbs. The data were modeled and visualized using co-occurrence graphs built with Java and Python.
The analysis reveals a semantic network comprising various lexical-semantic relations, including synonymy (7.27%), converse antonymy (31.32%), polysemy (2.21%), entailment (24.67%), hyponymy (22.46%), meronymy (2.21%), and collocation (34.49%). Among these, collocational patterns, antonymic contrasts, and entailment relations were most frequent. These results provide insights into the mental lexicon of L2 Persian learners, highlighting conceptual schemas and relational patterns. The study offers pedagogical implications for creating cognitively aligned teaching materials, addressing lexical acquisition gaps, and promoting cluster-based approaches in Persian as a Foreign Language curriculum development.
Keywords: Cognitive Linguistics, Lexical-Semantic Networks, Graph Theory, Second Language Acquisition, Persian as a Foreign Language (PFL)
 
Introduction
This article investigates and analyzes the semantic network of basic Persian verbs in the mental lexicon of non-Iranian learners of Persian. The study aims to identify how these learners—who have acquired Persian after their first language and beyond the critical period (as defined by Friederici, Steinhauer & Pfeifer, 2002, as ending around age twelve)—structure semantic relations among high-frequency Persian verbs. The research is framed within cognitive linguistics and lexical (cognitive) semantics. The experimental design is grounded in graph theory, utilizing Java and Python for graph construction and SPSS for statistical analysis.
Positioned within the domain of Persian language education, this study seeks to examine the conceptual and intra-linguistic relations among fifty high-frequency Persian verbs as structured by foreign learners. The significance of the research lies in its effort to compare the structural-semantic similarities of these learners’ mental lexicons with those of native speakers. The verbs were previously selected in Jamshidi et al. (2022), and the same experimental task used in that study was replicated here to enable a comparative analysis, aiming to uncover learning gaps among foreign learners. Since accurate mapping of semantic networks plays a crucial role in discourse coherence, the findings could inform methods to align foreign learners’ semantic networks more closely with those of native speakers.  
The main objective is to examine how learners conceptualize relations such as synonymy, antonymy, semantic entailment, collocation, and causality among these verbs, and how these relations manifest in their mental lexical networks. The study integrates perspectives from cognitive linguistics, lexical semantics, and computational linguistics while employing the analytical tools of graph theory to model and interpret the semantic connections formed by learners.
This study is guided by two principal research questions:    
1. What types of conceptual and intra-linguistic relations characterize the graph patterns constructed by non-native Persian learners?          
2. What are the structural features of their semantic networks for Persian basic verbs?

Materials & methods
The research adopts a field-based methodology using a questionnaire as the primary data collection instrument. A set of fifty verbs was selected through a comparative approach from the validated lists provided by Ebadi et al. (2014), Bijankhan et al. (2014), and Sahraee et al. (2017). Emphasizing frequency, as highlighted in these studies and also in Schur (2007), high-frequency verbs were randomly selected and presented to participants in the form of a questionnaire. Participants were instructed to identify semantic relationships among verbs. The collected data were then analyzed through graph visualization and interpretation.
 

Discussion
The findings reveal that the semantic networks constructed by non-native learners feature the following relational distributions: synonymy (7.27%), reversed antonymy (31.32%), polysemy (2.21%), semantic entailment (24.67%), hyponymy ("type of") (22.46%), meronymy ("part of") (2.21%), and collocation (34.49%). Among these, collocation, antonymy, and entailment occurred most frequently.       
Comparing the semantic graphs of native and non-native speakers shows that verbs such as raftan (to go), gereftan (to take), fahmidan (to understand), dādan (to give), and harekat kardan (to move) had the highest average degree in non-native learners’ graphs. In contrast, the highest-degree verbs in native speakers’ networks were anjām dādan (to do), fahmidan (to understand), raftan (to go), harekat kardan (to move), and resāndan (to deliver). The verbs fahmidan, raftan, and harekat kardan are shared among both groups, indicating partial overlap in semantic structuring.

Result
Step-by-step comparison of the semantic graphs of native speakers and foreign learners illuminated both their similarities and differences, highlighting strengths and weaknesses in learners’ mental lexicons. These insights suggest that incorporating semantic networks and conceptual schemas into educational materials for Persian learners can address persistent vocabulary learning challenges and improve verb substitution strategies. The study also identifies weaker areas among learners, such as polysemy, synonymy, meronymy, and causality, recommending deeper instructional focus on these relations in curriculum design.     
Pedagogical Recommendations          
1. To approximate the semantic networks of non-native learners to those of native speakers, workbook sections should include varied exercises demonstrating multiple senses of polysemous verbs, reinforced through repetition and contextual use.
2. When encountering negative transfer from the first language, instructors should employ contrastive analysis between Persian and the learners’ L1, using implicit corrective feedback strategies.
3. Greater emphasis should be placed on verb synonymy in Persian textbooks. Visual network mapping in classroom settings may leverage visual memory to reinforce learning and retention.