Degree centrality as a measure of robustness of dependency structures of the sentences in a large-scale learner corpus of E nglish (2025)

Abstract: This paper examines the differences in the robustness of syntactic dependency structures in written English produced by learners of varying proficiency levels and by native English speakers. The robustness of these dependency structures is represented by their degree centralities, and corpus-based investigation revealed that learners with higher proficiency levels tend to produce sentences with lower degree centralities. This means that they produce more robust, and more embedded sentences. It is also revealed that the sentences produced by native speakers of English tend to produce more embedded sentences than non-native speakers.

## introduction the aim of this paper is to examine the differences in the robustness of syntactic dependency structures in written english produced by learners of varying proficiency levels and by native english speakers. structural properties of sentences have been explored in the field of second language acquisition (sla) using a variety of metrics such as word per sentence or type-token ratio with the cover term of sentence complexity (e.g., @xcite @xcite @xcite @xcite @xcite @xcite . the basic tenet behind them is that the proficiency levels of learners can be represented by these metrics. in other words, it is expected that these metrics increase in proportion to the advancement of learners' proficiency levels. for example, @xcite pointed out that depth of clauses in the sentences produced by leaners of english increases in proportion to their proficiency levels, hence depth of clauses can function as a measure of sentence complexity. sentence complexity should not be regarded as a single independent variable, but as a dependent variable that can be represented by multiple variables (depth of clauses is one of them). in this context, it is essential to address these variables related to sentence complexity individually rather than treating them collectively and indiscriminately. by focusing on each factor in turn, we can understand the structural characteristics of the sentences produced by speakers/writers with certain attributes (e.g., native/non-native, beginners/intermediate/advanced, non-native with different backgrounds) more objectively. this paper introduces the robustness of dependency structures as one of these variables related to sentence complexity. specifically, i adopt degree centrality of the dependency structure of a sentence as a metric to measure its robustness. by modeling the dependency structures of english sentences in a corpus-organized by learners' proficiency levels-as graphs, i compute their degree centralities and investigate whether the distribution of these values reflects the learners' proficiency levels. this paper is organized as follows: section 2 summarizes the idea of dependency structures as graphs and their degree centralities, and explains the relationship between degree centralities of dependency structures and their robustness. in section 3, previous studies are briefly reviewed to point out their drawbacks. section 4 describes this study of degree centralities of english sentences in a large-scale learner corpus, which is followed by discussions in section 5. section 6 concludes this paper. ## dependency trees as graphs in network analysis, a graph consists of a collection of nodes and a set of edges linking these nodes @xcite . in this context, the degree of a node is determined by the number of edges connected to it. previous research @xcite @xcite has posited that the dependency tree (or structure) of a sentence can be conceptualized as a graph. more specifically, within a dependency tree, words function as nodes, while their dependency relationships are represented as edges, and the degree of a word is the number of other words depending on it and the word which it depends on. for example, an english sentence "i have written this article" has the dependency structure in the format of universal dependencies @xcite in figure 1 . the degree of the word "written" is four, because it depends on "root," and three words depend on it. graph theory establishes a variety of metrics that quantify the structural characteristics of graphs. if the dependency tree of a sentence is considered a specific type of graph, these metrics can be utilized to analyze its structural properties systematically. this approach enables a more objective and scientifically rigorous examination of its structure, as opposed to relying solely on intuitive interpretations. based on this premise, @xcite applied degree centrality @xcite as a metric to assess the complexity of dependency trees in english sentences (yet the use of the word "complexity" is rather problematic; discussed later). degree centrality is a type of index that indicates the significance of a given node within a specific graph. the degree centrality of a graph cd which contains g nodes is calculated by the following formula @xcite : in principle, degree centrality ranges from 0 to 1. if a graph has a degree centrality of 1, this signifies that a single node within the graph is connected to all other nodes, forming a star graph, as illustrated in figure 2 . the largest degree in the star graph in figure 2 is 4, which is the largest possible degree of a graph which contains 5 nodes. the degree of all the other nodes is 1. the enumerator and the denominator are the same, as indicated by the following formula, hence the degree centrality of the star graph is 1: 𝐶 𝐷 = (4-1)+(4-1)+(4-4)+(4-1)+(4-1) (4-1)+(4-1)+(4-4)+(4-1)+(4-1) = 1 degree centrality values decrease as the structure of graphs becomes more linear, meaning that no single node holds greater significance than the others. in figure 3 , the five nodes are arranged in a linear sequence (forming a line graph). the largest degree in the line graph in figure 3 is 2, and 3 of its nodes have that degree. the other 2 nodes have the degree 1. hence, the enumerator is 2. the denominator is the same as that of the star graph in figure 2 . therefore, as indicated by the formula (3), the degree centrality of the line graph in figure 3 is approximately 0.1667: the degree centrality of the example sentence "i have written this article" is calculated as follows: its dependency structure contains 6 nodes (including root). its largest observed degree is 4 (with written). one node has the degree 2 (with article), and all the other nodes have the degree one. the largest possible degree of a graph with 6 nodes is 5. therefore, as indicated by the formula (4), the degree centrality of the dependency structure of the example sentence is 0.7: 𝐶 𝐷 = (4-1)+(4-4)+(4-2)+(4-1)+(4-1)+(4-1) the degree centrality of a network (and a dependency structure of a sentence) is concerned with its robustness. sentences with larger degree centralities (with flatter dependency structure) contain a certain core word (or words) on which many of the other words in the same sentence depend. if the core word is deleted or overlooked, then the whole structure falls apart into unrelated words, and fails to be interpreted appropriately. on the other hand, sentences with lower degree centralities (with more embedded dependency structure) have no such core, or more than one core, and therefore, even if one of the words is deleted, there will be some fragments of structure which can be interpreted, though not completely. hence, sentences with lower degree centralities are more robust than those with higher degree centralities. it should be noted that the robustness of dependency structures as discussed here differs conceptually from syntactic robustness. ## previous studies some previous studies assume that the degree centrality values of sentences within a corpus can function as an indicator of their syntactic complexity, in which the word "complexity" is used as something represented by degree centrality. @xcite observed that the degree centrality values of english essays written by japanese learners tend to be higher than those of academic journal abstracts, suggesting that the former exhibit flatter and less embedded syntactic structures compared to the latter. @xcite conducted corpus-based research of degree centrality as a syntactic complexity measure. he revealed that sentences in different genres show different distributions of degree centralities, more specifically, sentences in fictions tend to have higher degree centralities than those in journals, meaning that the former have flatter syntactic structure than the latter. oya (2014) applied the idea of using degree centrality as a syntactic complexity measure into japanese, based on an english-japanese small-scale parallel corpus, and it is found that japanese sentences tend to have higher degree centralities than their english translations, meaning that japanese sentences are flatter than their english translations. the previous studies on the degree centralities of sentences contain the following two drawbacks: first, it is assumed that the degree centrality of a sentence can be used as a measure of its complexity without explicit explanation on why it can be. it is certain that structures with lower degree centralities are more robust, and it is found that the robustness is one of the characteristics of complex systems (e.g., @xcite ), yet it is not certain that more robust sentences are more complex. these previous studies should have used the word "robustness" instead of "complexity" of syntactic structure. second, there has been no study of degree centrality as a measure of structural robustness of english sentences generated by learners of english as a second language (l2) at different proficiency levels, let alone comparing and contrasting the degree centralities of english sentences generated by non-native speakers of english (non-ens) and those generated by native speakers of english (ens). in this context, this study is the first attempt to examine whether the degree centralities of sentences generated by non-ens in different proficiency levels show distributions which are different across these different proficiency levels, and from those by ens. if any difference between them is found, that will give us a new insight into the difference between non-ens and ens in terms of the robustness of the sentences they generate, based on the theoretical background of graph theory. ## this study the research question of this study is as follows: