Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

Degree Centralities, Closeness Centralities, and Dependency
Distances of Different Genres of Texts
Masanori Oya
Mejiro University
m.oya@mejiro.ac.jp

Abstract
This study investigates whether the directed acyclic graph representations of the typed-dependency trees forthe sentences (typed-dependency DAGs) in different genres of texts in the manually annotated sub corpus ofAmerican National Corpus (MASC 500k) show different distribution of their degree centralities, closenesscentralities and dependency distances. Different distributions of degree centralities and closeness centralities
are found among different genres, yet this can be considered to be a result of the fact that texts with shorter
sentences tend to have larger degree centralities and closeness centralities.

Keywords
Dependency grammar, Stanford Dependency Parser, Graph centralities

1

Introduction

Oya (2010b) showed that small-scale corpora of different genres of texts have different distributions ofdegree centralities and closeness centralities of the directed acyclic graph of the typed-dependency trees forthe sentences (typed-dependency DAGs: Oya2010a), and Oya (2011) showed that the corpora of the similar
scale have different distributions of dependency distances. This study uses a corpus larger than these corpora
used in Oya (2010b) and Oya (2011) in terms of the number of sentences, and wider in terms of genres, inorder to examine whether large-scale corpora of different genres of texts have different distributions ofdegree centralities, closeness centralities and dependency distances of the typed-dependency DAGs. Section
2 explains the background of this study; dependency grammar, graph centralities and dependency distance.
Section 3 deals with the analysis of data used in this study, and with the discussion of the results, and Section
4 concludes this study.

2

Background2.1
Dependency grammar
Lucien Tesnière, a French linguist in the 20th century, is considered to be the father of dependency grammar.
He argues that sentence structures are defined by the relationships between the head word and tail word; eachword in a sentence is dependent on another word, no word in a sentence is independent, and the dependency
relationship between words is characterized by a governor and a dependent (Tesnière 1959).
There are several different dependency-grammar frameworks based on Tesnière’s idea: Link Grammar(Sleator and Temperley 1991), Extensible Dependency Grammar (Debusmann 2003; Debusmann andKuhlmann 2007), Word Grammar (Hudson 2010), and Stanford Dependencies (de Marneffe and Manning2008).
The Dependency-grammar framework used in this study is Stanford Dependencies, because it is the
linguistic basis of Stanford Parser (de Marneffe and Manning 2006, 2008, and 2012) which I also use toparse a large number of sentences in the corpus in this study. Stanford Dependencies contain 55 dependency
types (de Marneffe and Manning 2012). For example, the figure below is the typed-dependency tree for asentence “Sarah has read this book.”
In this typed-dependency tree, the word “Sarah” depends on the verb “read”, and this dependency is typed as“NSUBJ”, which means “nominal subject”. The word “has” depends on “read” with the type “AUX”(auxiliary), the word “book” on “read” with the type “DOBJ” (direct object), and the word “this” on “book”
with “DET” (determiner). The main verb “read” depends on Root. The presence of Root in a
typed-dependency tree ensures that all the words in a sentence depend on another entity, and also reflects thedependency of the main predicate (“read” in the tree above) to a sentence-external, discourse level ofrepresentation.

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Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

Root
ROOT
PUNCT

.

read
NSUBJ
Sarah

DOBJ
AUX
has

book
DET
this

Figure 1: The typed-dependency tree for “Sarah has read this book.”
2.2
Typed-dependency trees as graphs
Oya (2010a, 2010b, and 2011) assume that the typed-dependency tree for a sentence can be considered to bea graph in the sense of graph theory which is a part of mathematics (Freeman, 1978; Wasserman & Faust,
1994). A graph consists of a set of vertices and a set of arcs connecting these vertices. An arc is directed if it
starts from one vertex to another. The number of arcs attached to a vertex is the degree of the vertex. In a
typed-dependency tree, each word in the tree is a vertex, and the dependency relation between words is an
arc which starts from the head to the tail. Each dependency relation is labeled with a dependency type whichindicates the function that the tail has with respect to the head of the dependency relation.
2.3
Graph centrality
In graph theory, various indices have been defined to show the structural property of a given graph. These
indices can be used to show the structural property of a given typed-dependency tree (Oya 2010b and 2011).
They allow us to understand the structural property of a given sentence more objectively. Among these
indices, Oya (2010b) proposed to use graph centrality for an index to show the complexity of
typed-dependency trees. Graph centrality shows the relative importance of vertices in a given graph(Freeman, 1978; Wasserman & Faust, 1994).
2.3.1
Degree centrality
Degree centrality indicates the extent to which the vertices in a graph are concentrated to one particularvertex. It is calculated by the following formula (Wasserman & Faust 1994: 180). The degree centrality of agiven graph (CD in the formula below) is the sum of the maximum degree in the graph minus the degree of
each of all the other vertices, divided by the largest possible sum of the maximum degree of the graph minus
the degree of all the other vertices. In the formula below, g is the number of vertices in a graph, CD(n*) is thelargest degree among the vertices in the graph, and CD(ni) is the degree of the ith vertex of the graph.
C =∑  ∑

∗


∗

 



(2.1)

 

The denominator equals the number of vertices minus 2 multiplied by the number of vertices minus one (SeeFreeman 1978).
The degree centrality of a given typed-dependency tree indicates how flat the tree is (Oya 2010b). The
flatness of a tree means the extent to which one particular word is the dependency head of other words.
Degree centrality increases in proportion to the flatness of typed-dependency trees. For example, consider
the example sentence “Sarah has read this book.” This sentence contains seven words, including Root andthe period. The maximum degree in the typed-dependency graph for this sentence is 5 at the word “read”; thesum of the maximum degree in the graph minus the degree of each of all the other vertices is(5-1)+(5-1)+(5-5)+(5-1)+(5-1)+(5-2)+(5-1)=23. The denominator is 30; hence the degree centrality of thetyped-dependency tree for the sentence “Sarah has read this book.” is 23/30⋍0.767.
Next, consider a sentence “Sarah would have read this book.” Figure 2 is the typed-dependency tree forthis sentence.

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Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

Root
ROOT
PUNCT

.

read
NSUBJ
Sarah

DOBJ
AUX
have

would

book
DET
this

Figure 2: The typed-dependency tree for “Sarah would have read this book.”
This sentence contains eight words, including the Root and the period. The maximum degree in thetyped-dependency tree for this sentence is 6 at the word “read”; the sum of the maximum degree in the graphminus the degree of each of all the other vertices is (6-1)+(6-1)+(6-1)+(6-6)+(6-1)+(6-1)+(6-2)+(6-1)=34.
The denominator is 42; hence the degree centrality of the typed-dependency tree for the sentence “Sarah
would have read this book.” is 34/42⋍0.81. As the degree centralities of these examples sentences show, a
typed-dependency tree with a flatter setting has a larger degree centrality.
Degree centralities of typed-dependency trees can indicate the flatness of sentences across languages.
Consider a typed-dependency tree for an English sentence in Figure 3 and its Japanese equivalent in Figure
4.
Root
ROOT
made
NSUBJ
Sarah

PUNCT
read
.
NSUBJ DOBJ
David
book
DET
the

Figure 3: The typed-dependency tree for “Sarah made David read the book.”

Root
ROOT
PUNCT .
yomaseta
TOPIC
Sarah-wa

POSTP_WO
POSTP_NI
David-ni
hon-woDET
kono

Figure 4: The typed-dependency tree for “Sarah-wa David-ni kono hon-wo yomaseta (Sarah made David
read this book.)”The degree centrality of the typed-dependency tree in Figure 3 is about 0.428, while that in Figure 4 is about
0.766. As this illustration suggests, the larger degree centrality of the typed-dependency tree in Figure 4
numerically indicates that this tree is flatter than its English counterpart.
2.3.2

Closeness centrality

Closeness centrality is defined as the reciprocal of the sum of the length of a path from one vertex to another44Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

in a graph (Freeman 1978; Wasserman and Faust 1994)1. This calculation is represented in the following
formula (Sabidussi 1966; Wasserman and Faust 1994: 184), in which g means the number of vertices (ornodes), and d(ni,nj) is the shortest path (geodesic distance) between the vertex ni and vertex nj.

C = n ∑



(2.2)

   , 

Wasserman and Faust (1994: 185) point out that the maximum value attained by the formula (2.2) above
depends on the number of vertices in a graph, and therefore it is difficult to compare values across networks
of different sizes. Therefore, they refer to Beauchamp (1965) which suggests to use standardized indicescalculated by the following formula.

C = n ∑! 

   ,

(2.3)



Wasserman and Faust (1994) point out that this can be viewed as the inverse average distance between vertex
i and all the other vertices, and it ranges from 0 to 1; it equals 1 when a vertex is adjacent (connected by oneedge) to all the other vertices.
In a typed-dependency tree representation for a sentence, the relevant length is that between the root andall the other words in the tree, because it represents the depth of embedding of each word from the root in thesentence (Oya 2010b).
Closeness centrality decreases in proportion to the embeddedness of typed-dependency trees. For example,
the example sentence “Sarah has read this book.” has six paths from the Root; Root-read, Root-read-Sarah,
Root-read-has, Root-read-., Root-read-book, and Root-read-book-this. The lengths of these paths are 1, 2, 2,
2, 2, and 3, respectively (the starting vertex is not included). The average length of them is 2, and thecloseness centrality of this sentence is the inverse of 2, that is, 0.5.
Next, consider an example sentence “My brother has read this book.” Figure 5 is the typed-dependency
tree for this sentence.
Root
ROOT
PUNCT

.

read
NSUBJ
brother
POSS

DOBJ
AUX
has

book
DET
this

My

Figure 5: the typed-dependency tree for “My brother has read this book.”
This sentence has seven paths from the Root; Root-read, Root-read-brother, Root-read-brother-My,
Root-read-has, Root-read-., Root-read-book, and Root-read-book-this. The lengths of these paths are 1, 2, 3,
2, 2, 2, and 3. The average length of them is 15/7⋍2.142, whose inverse is the closeness centrality of thissentence; 1/2.142⋍0.467.
Lastly, consider an example sentence “Sarah read the books David has.” Figure 6 is the typed-dependency
tree for this sentence.

1

Oya (2010b) proposed the term path length for the average length of a path from one given node to another in a graph.
However, unlike degree centrality, path lengths do not fall between 0 to 1. Therefore, Oya (2011) used the concept ofcloseness centrality as defined by Beauchamp (1965).

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Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics
Root
ROOT
read
NSUBJ
Sarah

PUNCT
DOBJ
books

.
RCMOD

DET
the

has
NSUBJ
David

Figure 6: The typed-dependency tree for “Sarah read the books David has.”This sentence has seven paths from the Root; Root-read, Root-read-Sarah, Root-read-books-the,Root-read-books, Root-read-books-has-David, Root-read-books-has, and Root-read-.. The lengths of thesepaths are 1, 2, 3, 2, 4, 3, and 2. The average length of them is 17/7⋍2.44, whose inverse is the closenesscentrality of this sentence; 1/2.44⋍0.41. As the closeness centralities of these example sentences show, a
typed-dependency tree with a more embedded setting has a smaller closeness centrality.
Oya (2010b) showed that the distributions of degree centralities and that of closeness centralities of thesentences in different small-sized corpora (English essays written by Japanese university students, abstractsof academic journals, and the 1st chapter of “The Golden Bough”) are different: the English essays tend tocontain sentences with larger degree centralities than the abstracts; the abstracts tend to contain sentenceswith smaller closeness centralities than the English essay.
2.4
Dependency distanceThe drawback of Graph-centrality measures for sentence complexity is that they do not show the dependency
distance between the head and the tail of a dependency relation because they abstract away the linear orderof words in a sentence (Oya 2011). Dependency distance is defined as the number of words between the head
and the tail of a dependency relation, and the average dependency distance of a sentence is the sum of all thedependency distance divided by the number of dependency relations. For example, in the typed-dependency
tree in Figure 1, the dependency distance between the word “Sarah” and “read” is 2, “has” and “read” is 1,“book” and “read” is 2, “this” and “book” 1, “read” and “.” is 4. The Root is considered as the 0th word;hence the dependency distance between “Root” and “read” is 3. The average dependency distance of thesentence “Sarah has read this book.” is (2+1+2+1+4+3) / 6⋍2.167.
Dependency distance of a given typed-dependency tree can be employed to indicate the complexity of thetree. With respect to dependency distance, Gibson (1998, 2000) argued that the syntactic complexity ofsentences increases in proportion to the dependency distance, and Temperley (2006) proposed the presenceof preference for longer or shorter dependency distances according to different syntactic contexts. Oya(2011) argued that the average dependency distance of the sentences can be applied to calculate the sentencecomplexity of the English sentences written by native speakers of English and that of those written by
non-native speakers of English, and conducted an analysis of average dependency distance of sentences insmall-sized corpora taken from different types of writers (English textbooks for Japanese high schools,
English essays written by Japanese university students, and newspaper articles). The results showed that the
average dependency distance of the sentences in newspaper articles is the largest among these three corpora.
2.5
Related work
Since the seminal work by Biber (1988), there have been a number of attempts to use syntactic features forgenre classification. For example, part-of-speech trigrams are used by Argamon et al. (1998), and Santini(2004) applied their method to ten different genres in BNC. Their method uses only shallow syntactic
information (POS tags), and it is expected that deep syntactic information will also be effective for genre
classification. Deep syntactic information includes the dependency structure of a sentence in terms of degree
centrality and closeness centrality, and the average dependency distances of a sentence.

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Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

3

Data analysis

3.1
Data description
The corpus used in this study is the manually annotated sub corpus of American National Corpus (MASC500k). This corpus contains approximately 500,000 words of contemporary American English, drawn fromOpen American National Corpus (OANC) (Ide and Suderman 2004). MASC 500k covers a wide range ofgenres: blogs, essays, fictions, short fictions taken from a website Ficlet (now closed), government
documents, jokes, journals, newspapers, non-fictions, technical reports, and travel guides. Texts of emails,
spam emails, movie scripts, speeches, and debates are also included, but not included in this study. Table 1
shows the descriptive statistics of the sentence numbers, word counts and words per sentence (WPS) of eachgenre.
Table 1: The total number of sentences, the total number of words and the mean length of a sentence in eachgenre
Subsections
Blog
Essay
Ficlets
FictionGovt-doc
Jokes
JournalNews
Non-Fiction
Technical
TravelGuide
Total

Sentences

Words

1524
1072
2645
2639
1028
2254
867
1196
1278
825
1196
16524

WPS Mean

28381
27367
30555
37531
24277
31751
21997
26877
26441
19787
24187
299151

18.62
25.52
13.34
14.22
23.61
14.08
25.37
22.47
20.68
23.98
20.23

WPS S.D.
12.34
13.18
7.15
8.32
12.55
8.6
14.45
10.43
11.41
13.58
8.6

The subsections Fiction, Ficlets and Jokes show relatively smaller mean WPSs compared to othersubsections. Their standard deviations are also smaller than those of other sections. The subsection Essay has
the largest WPS among them.
3.2
Method and Results
The raw texts in each of the genres without tags (downloaded as a data-only file from the website of ANC:
http://www.anc.org/MASC/Download.html) are parsed by Stanford Parser, and the degree centrality,
closeness centrality and dependency distance of the parse-output typed-dependency DAGs for the sentencesin the texts are calculated automatically by scripts written in Ruby. Table 2 shows the descriptive statistics ofdegree centralities, closeness centralities and average dependency distance of each genre. The results showthat different genres of texts show different distribution of degree centrality, closeness centrality and averagedependency distance.
Table 2: Descriptive statistics of degree centralities, closeness centralities, and dependency distance
Blog
Essay
Ficlets
FictionGovt-doc
Jokes
JournalNews
Non-Fiction
Technical

Degree
Mean
0.43
0.26
0.57
0.54
0.26
0.51
0.27
0.27
0.37
0.32

S.D.
0.26
0.19
0.29
0.27
0.18
0.27
0.19
0.17
0.22
0.22

Closeness
Mean
0.39
0.32
0.47
0.43
0.33
0.44
0.33
0.33
0.36
0.34

S.D.
0.12
0.09
0.11
0.11
0.10
0.13
0.09
0.09
0.10
0.12

Dep.Dist.
Mean
2.99
3.58
2.31
2.65
3.41
2.55
3.63
3.34
3.20
3.37

S.D.
1.19
1.09
1.01
1.05
1.12
1.15
1.35
0.94
1.07
1.27

The subsections Ficlets, Fiction and Jokes are the three subsections with the top-three largest mean degree
centrality. Their standard deviations are also larger than those of other sections. The subsection Essay shows
the smallest degree centrality among them.

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Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

The subsections Ficlets, Fiction and Jokes are the three subsections with the top-three largest mean
closeness centrality. The standard deviation of Jokes is the largest of them, but those of Blog and Technicalare larger than those of Ficlets and Fiction.
The subsections Fiction, Ficlets and Jokes are the three subsections with the top-three shortest dependency
distance. The subsection Journal has the longest dependency distance. The subsection Journal has the largest
standard deviation, and News the smallest.
Example typed-dependency trees taken from these subsections will illustrate the claim that flatter trees
have larger degree centralities and more embedded trees have smaller closeness centralities. For example,
Figure 7 below is the typed-dependency tree for an example sentence selected from the subsection Journal.
This has 10 words. Its degree centrality is about 0.722, its closeness centrality is about 0.473, and its averagedependency distance is about 2.444.
Root-0ROOT
made-4PUNCT
ADVMOD
PUNCT
Now-1
,-2

.-9

PREP
NSUBJ
it-3

DOBJ
sense-6
DET

at-7
POBJ

no-5

all-8

Figure 7: The typed-dependency tree for “Now, it made no sense at all.”Figure 8 is the typed-dependency tree for another example sentence selected from the subsection Journal.
This has 10 words. Its degree centrality is about 0.444, its closeness centrality is 0.391, and its averagedependency distance is about 2.333.
Root-0ROOT
moved-2

NSUBJ
They-1PUNCT
XCOMP
ADVMOD
westward-3
start-5
AUX
DOBJ
to-4
DET
a-6

.-9

life-8AMOD
new-7

Figure 8: The typed-dependency tree for “They moved westward to start a new life.”
Figure 9 is the typed-dependency tree for an example sentence selected from the subsection Blog. This has
10 words. Its degree centrality is about 0.722, its closeness centrality is 0.45, and its average dependency
distance is about 2.666.

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Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics
Root-0

lie-5
PUNCT
.-9
NSUBJ

This-1RCMOD
DET AMOD
the-3
big-4

COP
is-2

tell-8NSUBJ

wholesalers-7
DET
the-6

Figure 9: The typed-dependency tree for “This is the big lie the wholesalers tell.”Figure 10 is the typed-dependency tree for another example sentence selected from the subsection Blog.
This has 10 words. Its degree centrality is about 0.305, its closeness centrality is 0.36, and its averagedependency distance is about 2.555.
Root-0
ROOT
is-2
PUNCT
EXPL
NSUBJ
thing-5

There-1
DET
no-3

AMOD
such-4.-10
PREP_ASflowers-9
AMOD
many-8ADVMOD
too-7

Figure 10: The typed-dependency tree for “There is no such thing as too many flowers.”
The degree centralities, closeness centralities, and average dependency distances of these example
typed-dependency trees are shown in Table 3 below. The typed-dependency tree in Figure 7 is as flat as thatin Figure 9, because they have the same degree centrality. The typed-dependency tree in Figure 7 is the least
embedded than others, because it has the largest closeness centrality among them. The typed-dependency
tree in Figure 10 is the least flat and the most embedded one among them, because it has the smallest degree
centrality and the smallest closeness centrality. The average dependency distances of these typed-dependency
trees do not seem to be as different as their degree centralities and their closeness centralities.
Table 3: The degree centralities, closeness centralities, and average dependency distances of the example
typed-dependency trees
DegreeFigure 7
Figure 8
Figure 9
Figure 10

Closeness
0.722
0.444
0.722
0.305

Dep.Dist
0.473
0.391
0.450
0.360

2.444
2.333
2.666
2.555

The larger degree centrality and closeness centrality of the sentences in Fiction, Ficlet and Jokes can be theresult of the fact that they contain sentences shorter than those in other genres on average, as their WPSs
indicate; degree centrality tends to become smaller in proportion to the number of words in sentences(Satoshi Yoshida, p.c.). This suggests that the difference of distributions of degree centrality and closeness49

Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

centrality among sentences in different genres is nothing but a paraphrase of different distribution of WPSs
among these sentences. In order to address this issue, it will be desirable to treat degree and closenesscentrality with precaution; for example, controlling the number of words in a sentence to examine how both
centralities of the sentences of equal word count show different distributions. Figure 11 is the distribution ofdegree centralities of 10-word sentences in each genre of MASC500k, and Figure 12 is the distribution ofdegree centralities of 20-word sentences in the same corpus.

Occurrences50
blog(n=58)

40
30

essays (n=11)

20
ficlets (n=170)

10
0
0

0.5

1

fiction (n=160)

Degree centralities

Occurrences

Figure 11: the distribution of degree centralities of 10-word sentences in each genre of MASC500k
45
40
35
30
25
20
15
10
5
0

blog (n=43)
essays (n=45)
ficlets (n=37)
fiction (n=71)
0

0.5

1

govt (n=40)

Degree centralities

Figure 12: the distribution of degree centralities of 20-word sentences in each genre of MASC500k
Notice that the distribution of degree centralities of 10-word sentences are more dispersed than that of
20-word sentences, and in the distribution of 20-word sentences, there is only a small number of degree
centralities more than 0.5.
Sentences in different genres show different distributions of degree centralities. We can see the difference
more explicitly if we look at one particular degree centrality across different genres. For example, let us
concentrate on Fiction and Journal. 39 sentences of all the 10-word sentences in Fiction (n=160) have thedegree centrality 0.72. This means that about 24% of these sentences in Fiction have the degree centrality
0.72.
On the other hand, 2 sentences of all the 10-word sentences in Journal (n=28) have the degree centrality
0.72. This means that about 7% of 10-word sentences in Journal have the degree centrality 0.72. These
results suggest that sentences in Fiction tend to be flatter than those in Journal, as far as 10-word sentences inthese genres are concerned.
17 sentences of all the 20-word sentences in Fiction (n=71) have the degree centrality 0.35. This meansthat about 24% of these sentences in Fiction have the degree centrality 0.35. On the other hand, 1 sentence of
all the 20-word sentences in Journal (n=35) has the degree centrality 0.35. This means that about 2% of thesesentences in Journal have the degree centrality 0.35. Again, these results suggest that sentence in Fiction tend
to be flatter than those in Journal, as far as 20-word sentences are concerned.
The distributions of closeness centralities of the sentences of the same word count are somewhat different
from those of degree centralities. Figure 13 is the distribution of closeness centralities of 10-word sentences,and Figure 14 is the distribution of closeness centralities of 20-word sentences.

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35
blog (n=58)

Occurrences

30
25

essay (n=11)

20
15

ficlets (n=170)

10
fiction (n=160)

5
0
0

0.5

1

govt-docs (n=32)

Closeness centralities

Figure 13: the distribution of closeness centralities of 10-word sentences in each genre of MASC500k
35
blog (n=43)

30
25

essays (n=45)

20
ficlets (n=37)

15

fiction (n=71)

10
5

govt-docs (n=40)

0
0

0.5

1

Figure 14: the distribution of closeness centralities of 20-word sentences in each genre of MASC500k
Notice that the distribution of closeness centralities of 10-word sentences are more dispersed than that of
20-word sentences, and there is no closeness centrality more than 0.5 in the distribution of 20-word
sentences. On the other hand, the number of different closeness centralities increases in proportion to theincrease in the word counts; for example, as for the 10-word sentences in Fiction, there are 11 different
values of closeness centralities, while for the 20-word sentences in Fiction there are 26 different values ofcloseness centralities. The closeness centralities of 10-word sentences and those of 20-word sentences in
Fiction are shown in Tables 4 and 5 below.
Table 4: the different values of closeness centrality and the number of sentences which have the samecloseness centrality value (10-word sentences)
Closeness
0.35710.37040.38460.40000.41670.43480.45450.47620.50000.52630.5556

Sentences
1
3
2
5
14
17
25
25
33
24
11

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Selected Papers of the 17th Conference of Pan-Pacific Association of Applied Linguistics

Table 5: the different values of closeness centrality and the number of sentences which have the samecloseness centrality value (20-word sentences)
Closeness
0.23530.23810.25640.26320.27030.27400.28570.29410.29850.30300.30770.31250.3175

Sentences
1
1
1
1
3
1
1
4
2
4
1
2
6

Closeness
0.32260.33330.33900.34480.35090.35710.36360.37040.37740.3846
0.39220.40000.4082

Sentences
2
2
3
2
2
5
1
6
4
7
5
2
2

As is the case in degree centralities, sentences in different genres show different distributions of closenesscentralities. As for the closeness centralities of 10-word sentences, Fiction has 33 10-word sentences with thecloseness centrality 0.384 out of 160 (about 20%), while Journal has 2 10-word sentences with the samecloseness centrality out of 28 (about 10%). These results suggest that sentences in Journal tend to be more
embedded than those in Fiction. As for the closeness centralities of 20-word sentences, there is not the samevalue of closeness centrality which is found in Fiction and Journal.
3.3
Discussion
The distributions of degree centralities and that of closeness centralities suggest that the degree centrality andthe closeness centrality of a sentence are dependent on the word count of the sentence; the increase in word
counts results in smaller degree centralities and closeness centralities, and it also results in more diverse
values of closeness centralities. However, if we control the word count of the sentences taken from different
genres, we can make explicit that the difference in genre is reflected on the number of sentences of the same
degree centrality and of the same closeness centrality. In order to have a broader understanding of theirdistributions, we need to explore the difference of them across different word counts and different genres,
which will be the research topic in future.

4

Conclusion

This study demonstrated that different distributions of degree and closeness centralities are found among
different genres in MASC500k, yet it is suggested that this result can be due to the fact that texts with shorter
sentences tend to have larger degree centralities and closeness centralities. It is also suggested that degreeand closeness centrality should be treated with precaution. The distributions of degree centralities andcloseness centralities of the sentences with the same word count taken from difference genres of corpus
seemed to reflect the difference of these genres. Further examinations of the degree centralities and closenesscentralities of the sentences in a variety of genres will enable us to have a broader understanding of theirdistributions, which will be addressed in future research.
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