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Modeling the Fluctuation Patterns of Monthly

Inbound Tourist Flows to China: A Complex

Network Approach

Yongrui Guoa, Jie Zhanga, Yang Yangb & Honglei Zhanga

a Department of Land Resources and Tourism Sciences, Nanjing University,

Nanjing, Jiangsu, People's Republic of China

b School of Tourism and Hospitality Management, Temple University,

Philadelphia, PA, USA

Published online: 26 Aug 2014.

To cite this article: Yongrui Guo, Jie Zhang, Yang Yang & Honglei Zhang (2015) Modeling the Fluctuation

Patterns of Monthly Inbound Tourist Flows to China: A Complex Network Approach, Asia Pacific Journal of

Tourism Research, 20:8, 942-953, DOI: 10.1080/10941665.2014.948024

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Modeling the Fluctuation Patterns of Monthly

Inbound Tourist Flows to China: A Complex

Network Approach

Yongrui Guo

1

, Jie Zhang

1

, Yang Yang

2

and Honglei Zhang

1

∗

1

Department of Land Resources and Tourism Sciences, Nanjing University, Nanjing, Jiangsu,

People’s Republic of China

2

School of Tourism and Hospitality Management, Temple University, Philadelphia, PA, USA

A thorough understanding of the ﬂuctuations of tourist ﬂows provides useful insights con-

cerning the nature of tourist demand. This study aims to investigate the ﬂuctuation pat-

terns and dynamics of inbound tourist ﬂows to China using a complex network

approach. Several measures, such as the network topological parameters of degree and

degree distribution, betweenness centrality, and shortest path length, are utilized to dis-

cover important ﬂuctuation patterns and the transition distance. Based on the empirical

results, six important ﬂuctuation patterns of inbound tourist ﬂows to China are recog-

nized. These ﬂuctuation patterns are important intermediaries in the process of transform-

ation of the ﬂuctuation patterns and can be viewed as a prelude to changes in the inbound

tourist ﬂows. The value of 3.38 found for the average transition distance suggests that the

transformation occurs approximately every three to four quarters. These ﬁndings are

useful for understanding the inherent laws and transformations governing ﬂuctuations

in tourist ﬂows.

Key words: inbound tourist, tourist ﬂows, ﬂuctuation patterns, complex network, China

Introduction

Since China adopted the “open-door” policy

in 1978, tourism, especially inbound tourism,

has developed rapidly (Yang & Wong,

2013). In 1986, tourism, as an economic

industry, was incorporated for the ﬁrst time

into the ﬁve-year state plan for the National

Economy and Social Development; in 1992,

tourism was included as one of the key indus-

tries in the tertiary sector; in 1998, tourism

was selected as a new growth pole of the

national economy; and in 2009, the State

Council of the People’s Republic of China

Asia Paciﬁc Journal of Tourism Research, 2015

Vol. 20, No. 8, 942–953, http://dx.doi.org/10.1080/10941665.2014.948024

∗Corresponding author. Email: zhanghonglei@nju.edu.cn

#2014 Asia Paciﬁc Tourism Association

Downloaded by [Stephen F Austin State University] at 04:23 05 August 2015

issued a directive to upgrade tourism to a stra-

tegic pillar industry in the national economy.

Inbound tourist ﬂows to China increased from

27.46 million in 1990 to 132.40 million in

2012, representing an annual growth rate of

more than 7.4% (CNTA, 2013). Inbound

tourism, with its important role in securing

foreign exchange earnings, is of great impor-

tance to the economy of China (Yang &

Wong, 2013). Inbound tourism receipts

increased from US$2,217.58 million in 1990

to US$50,028.00 million in 2012 (CNTA,

2013). In view of the rapid increase in

inbound tourist ﬂows and receipts over the

past few decades, a comprehensive examination

of ﬂuctuations of inbound tourist ﬂows is of

importance to both tourism business prac-

titioners and tourism policy-makers. In this

article, we introduce a complex network

approach to model the ﬂuctuation patterns of

monthly inbound tourist ﬂows to China.

Temporal ﬂuctuations of tourist ﬂows trig-

gered by seasonality and business cycles are

one of the most signiﬁcant characteristics of

tourism (Assaf, Barros, & Gil-Alana, 2011;

Cuccia & Rizzo, 2011; Fourie & Santana-

Gallego, 2011;Nadal,Font,&Rossello,

2004; Song & Li, 2008;Vergori,2012). Over

the past three decades, many studies on

tourism demand analysis and forecasting have

contributed signiﬁcantly to our understanding

of the temporal ﬂuctuations of tourism

demand (Song, Li, Witt, & Athanasopoulos,

2011). However, although the importance of

temporal ﬂuctuations of tourist ﬂows has been

broadly recognized, it has also been acknowl-

edged that this phenomenon is not well under-

stood (De Cantis, Ferrante, & Vaccina, 2011;

Higham & Hinch, 2002;Jang,2004;Lim&

McAleer, 2001). Most existing studies of

tourism demand have involved a forecasting

perspective, and fewer studies have focused

on the ﬂuctuation patterns of tourist ﬂows

(Chan, Lim, & McAleer, 2005;Cho,2009).

An in-depth understanding of the ﬂuctuations

of tourist ﬂows is the basis for accurate predic-

tions of future trends in tourism demand. It is

important to scrutinize changes in both the

patterns and the amplitude of ﬂuctuations (De

Cantis et al., 2011). The aim of this study is

to examine the ﬂuctuation patterns, amplitude,

and dynamics of monthly inbound tourist ﬂows

to China from January 1990 to December 2012

using a complex network approach.

The paper is organized as follows. After this

introductory section, we brieﬂy outline the

recent literature relating to the study of

tourism demand. The subsequent section

describes our methodology and data source.

Using a complex network approach, we

analyze the ﬂuctuation patterns, amplitude,

and dynamics of inbound tourist ﬂows to

China. The results are presented in the next

section, and some concluding remarks are

offered in the ﬁnal section.

Literature Review

Tourism demand forecasting is one of the most

important task for planning development and

operational management in the tourism indus-

try. Exploring the ﬂuctuation patterns and

accurately forecasting the future tourist ﬂows

are essential to determine successful invest-

ments for both the public and the private

sectors (Chang & Liao, 2010). The information

from these investigations and forecasts plays a

highly important role in formulating national

tourism development policy and strategic plan-

ning, optimizing allocation of tourism market

resources, and conducting decision-making for

tourism businesses (Tao & Ni, 2010).

Measuring and analyzing ﬂuctuation is an

important aspect of the study of tourism

demand (Chu, Yeh, & Chang, 2014;Turner

Modeling the Fluctuations of Tourist Flows 943

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&Witt,2001). Gil-Alana (2005) examined

monthly international tourist ﬂows in the USA

by assuming seasonal univariate long-memory

processes and suggested that the total number

of arrivals implied long memory and mean

reverting behavior. Shareef and McAleer

(2005) analyzed the conditional volatility of

tourist ﬂows to small island tourism economies

and found that the logarithm of monthly inter-

national tourist arrivals was stationary. Yan

and Wall (2003) identiﬁed the structure, charac-

teristics, and intensity of ﬂuctuations in the

number of international visitors to China from

1980 to 1998 and showed that the overall

trend was strong annual growth, inﬂuenced by

a cyclical ﬂuctuation. Several studies have

applied sophisticated methods for forecasting

tourism demand, such as the space– time

cluster approach (Gursoy, Parroco, & Scuderi,

2013), multivariate exponential smoothing

(Athanasopoulos & de Silva, 2012), evolution-

ary fuzzy systems (Hadavandi, Ghanbari, Sha-

hanaghi, & Abbasian-Naghneh, 2011), the

autoregressive integrated moving average

model (Coshall, 2006; Gustavsson & Nord-

strom, 2001), dynamic almost ideal demand

system approach (Kuo, Liu, & Chen, 2014),

the seasonal autoregressive integrated moving

average model (Goh & Law, 2002), the vector

autoregressive model (Song & Witt, 2006), the

autoregressive distributed lag model (Song,

Lin, Zhang, & Gao, 2010), the Lagrange multi-

plier unit root tests (Lean & Smyth, 2009), and

time-varying parameter error correction model

(Li, Wong, Song, & Witt, 2006). Several

studies have also compared the forecasting

accuracy of various models and approaches

(Cho, 2003; Kim & Moosa, 2001; Wong,

Song, Witt, & Wu, 2007). Two extensive

reviews in this area are available from Song

and Li (2008) and Li, Song, and Witt (2005).

Identiﬁcation of the ﬂuctuation character-

istics of time series data is of crucial impor-

tance in a wide variety of ﬁelds. Many

methods, such as the Lyapunov exponent,

the autoregressive conditional heteroscedasti-

city model, and the stochastic volatility

model, have been used to analyze these charac-

teristics. These traditional methods focus

primarily on the overall features of the time

series but cannot provide nuanced information

on the determinations of the system properties

(Yang, Pan, & Song, 2014;Zhang,Zhou,

Jiang, & Wang, 2010). The study of time

series data using a complex network approach

has attracted great interests among scholars.

Time series can be mapped as a complex

network using various methods, such as the

visibility graph algorithm (Lacasa, Luque, Bal-

lesteros, Luque, & Nuno, 2008) and the

coarse-graining process (Li & Wang, 2007).

Through the application of the complex

network approach, the temporal dynamics of

time series data is encoded into the topology

of the corresponding networks. According to

the statistical properties of the network, the

determinations of different ﬂuctuation patterns

can be identiﬁed (Zhang et al., 2010). In ﬁnan-

cial time series, for example, Bonanno et al.

(2004)showed that a network can be obtained

by a correlation-based ﬁltering procedure and

that meaningful economic information can be

extracted from noise-dressed correlation

matrices. Fluctuations or temporal imbalances

in tourist ﬂows create an evolving complex

dynamic system. In nature and society, many

complex dynamic systems can be represented

as complex networks (Li & Wang, 2007).

Complex network approach offers a promising

new method to the analysis of tourist ﬂow time

series data.

In this paper, we develop a weighted

network of monthly inbound tourist ﬂows to

China from January 1990 to December

2012. The network can translate inbound

tourist ﬂows to various characteristics in its

944 Yongrui Guo et al.

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network topological structure. Every node

in the network corresponds to a distinct

ﬂuctuation pattern and has a special role in

shaping the dynamics of inbound tourist

ﬂows. We introduce several effective par-

ameters for detecting important topological

nodes of the network of inbound tourist

ﬂows. From these nodes, we can obtain signiﬁ-

cant ﬂuctuation patterns of inbound tourist

ﬂows to China. We focus on the ﬂuctuations

and correlations of changes in inbound

tourist ﬂows. The statistical properties of ﬂuc-

tuations in inbound tourist ﬂows are impor-

tant for understanding and modeling the

complex dynamics of inbound tourist ﬂows.

Data Source and Methodology

Data Source

The monthly time series data for inbound

tourist ﬂows to China used in the present

study were obtained from The yearbook of

China tourism statistics (1991–2013). The

series contains 276 data points from January

1990 to December 2012 (Figure 1). The term

“inbound tourists” to China refers to foreign

tourists and tourists from Hong Kong,

Macau, and Taiwan. The time series of

inbound tourist ﬂows to China was rep-

resented as T(t)(t¼1, 2, 3, ...,N,N¼276).

Coarse-Graining Preprocess

The simplest possible method for transforming

a time series into a complex network represen-

tation is to coarse grain its range into a suitable

set of classes and to consider the transition

probabilities between these classes in terms

of a weighted network. The coarse-graining

process is an effective method for analyzing

the complexity of time series data. After a

time series interval has been divided into

homogeneous partitions, the interval can be

averaged into limited subintervals (Li &

Wang, 2007). By giving each subinterval a

symbol, the time series data can be represented

as a discrete symbolic sequence; studying the

time series is then equivalent to studying

the symbolic sequence. The coarse-graining

process maintains the ﬂuctuation trajectory

regardless of the time series data; therefore,

Figure 1 Monthly Inbound Tourist Flows to China from January 1990 to December 2012.

Modeling the Fluctuations of Tourist Flows 945

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the process aids in studying the complexity of

the time series data (An, Gao, Fang, Huang, &

Ding, 2014). The time series of inbound

tourist ﬂows to China can be transformed

into a more understandable and limited sym-

bolic sequence using the coarse-graining

process. In this symbolic sequence, each

symbol denotes a distinct ﬂuctuation pattern.

In the coarse-graining process, symbolic cat-

egories should be limited, and each symbol rep-

resents a distinct meta-pattern of ﬂuctuation of

inbound tourist ﬂows. The meta-pattern refers

to the distinct symbols in a symbolic sequence

(Li & Wang, 2006a). For inbound tourist

ﬂows to China T(t), the ﬂuctuation is

DT=Tt−Tt−1. The average monthly change

in inbound tourist ﬂows to China from January

1990 to December 2012 is 487,690. We then

deﬁne four distinct symbols as follows:

Si=

R(DT≥487690),

r(0,DT,487690),

d(−487690 ,DT,0),

D(DT≤−487690),

⎧

⎪

⎪

⎨

⎪

⎪

⎩

(1)

where Ris a sharp-increase meta-pattern, ris a

small-increase meta-pattern, dis a small-

decrease meta-pattern, and Dis a sharp-

decrease meta-pattern. Here, R,r,d,andDare

measurements of the magnitude of the increase

and decrease of the ﬂuctuations in inbound

tourist ﬂows to China. Therefore, the time

series data of inbound tourist ﬂows to China

are transformed into a symbolic sequence:

S={S1S2S3···},Si[(R,r,d,D).(2)

Network Construction

We can obtain various string combinations

using the distinctive symbols (R,r,d,D).

Each string of symbols denotes a distinct ﬂuc-

tuation pattern of inbound tourist ﬂows to

China. We deﬁne an n-string as a string

composed of nsymbols. For a given n, there

are a total of 4

n

different n-strings. In coarse-

graining processing, redundant information

increases as the number of symbol strings

increases (Li & Wang, 2006b). For this

reason, we deﬁned three months (a quarter) as

a ﬂuctuation pattern of inbound tourist ﬂows

to China. The ﬂuctuation patterns of inbound

tourist ﬂows to China were 3-symbol strings

composed of R,r,d,andD. Therefore, the

ﬂuctuation patterns and dynamics of inbound

tourist ﬂows to China were investigated for

each six-month period. Because n¼3, 4

3

¼

64 3-strings, that is, (RRR,RRr,RRd,RRD,

RrR,RdR,RDR,... ), are theoretically poss-

ible. However, only 28 types of 3-strings actu-

ally appear. In symbol sequences of inbound

tourist ﬂows to China, the 3-strings can rep-

resent different ﬂuctuation patterns.

According to formulas (1) and (2), the

symbolic sequence of inbound tourist ﬂows

to China is written in the form

{rDRrddrrdrdrdrrdddrrdrdrdrrrdd ... }. The

ﬂuctuation patterns of inbound tourist ﬂows

P

i

can be calculated by applying the following

formula:

Pi=(S3∗i−2,S3∗i−1,S3∗i).(3)

According to formula (3), the ﬂuctuation pat-

terns of inbound tourist ﬂows to China can be

expressed as {rDR,rdd,rrd,rdr,drr,ddd,rrd,

rdr,drr,rdd,... }. That is, the ﬂuctuation pat-

terns evolve into each other with time {rDR

rdd rrd rdr drr ddd rrd

rdr drr rdd ... }. To identify the rule

of the transformation and detect signiﬁcant

ﬂuctuation patterns, we draw on complex

network theory to construct a weighted

network of inbound tourist ﬂows to China.

The main idea of complex network theory is

946 Yongrui Guo et al.

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to consider the relationships between various

parts of real complex systems as a complex

network (An et al., 2014). By analyzing the

structure of the network, we can better under-

stand the essential characteristics of the real

systems. In the symbolic sequence of ﬂuctu-

ation patterns in inbound tourist ﬂows to

China, the ﬂuctuation patterns are deﬁned as

nodes of the network, the transformations are

deﬁned as edges, and the weight of an edge is

the number of transformations between the

two types of ﬂuctuation patterns. The corre-

sponding network is shown in Figure 2.

Empirical Results

Important Fluctuation Patterns

We identiﬁed the signiﬁcant ﬂuctuation

patterns in the network of inbound tourist

ﬂows using the degree and degree distribution

parameters of the complex network. The

concept of degree is the most fundamental

characteristic and measure of a node in a

network. The degree of a node in a complex

network is deﬁned by the number of edges

directly connecting it to its neighbor. In this

paper, a node situated next to a given node is

considered its neighbor. The average degree

of a network is the average value of all node

degrees over the entire network. In undirected

networks, degree is a single number, but in

directed networks, nodes have two different

degrees, an in-degree and out-degree, corre-

sponding to the number of edges pointing

inward to and outward from those nodes. In

most cases, a node of higher degree is more

important than one of lower degree in a

network because it will have a more signiﬁcant

inﬂuence on other nodes in the network in

terms of dynamics, information ﬂows, and

data trafﬁc, among other variables (Chen,

Wang, & Li, 2012). In this paper, the

Figure 2 The Weighted Network of Fluctuation Patterns in Inbound Tourist Flows to China.

Note: The greater the transition frequency, the thicker the line between nodes.

Modeling the Fluctuations of Tourist Flows 947

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network of inbound tourist ﬂows is a directed

network. The in-degree of the network of

inbound tourist ﬂows represents other ﬂuctu-

ation patterns transformed into a special

ﬂuctuation pattern. The out-degree of the

network of inbound tourist ﬂows represents

a special ﬂuctuation pattern transformed into

other ﬂuctuation patterns. Because the edge

is the sequential transformation between the

two nodes, the out-degree and in-degree of

each node are equal except for the ﬁrst and

last nodes. In this paper, we use the out-

degree of the nodes to describe the degree

and degree distribution of the network of

inbound tourist ﬂows. The degree distribution

of the network of inbound tourist ﬂows can be

deﬁned as follows:

p(k)=Ni

N,(4)

where N

i

denotes the number of nodes whose

degree equals kand Ndenotes the total

number of nodes in the network. A larger

out-degree of a special ﬂuctuation pattern

implies a greater probability that this ﬂuctu-

ation pattern will transform into another

pattern directly rather than through a series

of intermediate ﬂuctuation patterns. A ﬂuctu-

ation pattern of higher degree is more impor-

tant than one of lower degree.

We calculated the degree of every node in

the network of inbound tourist ﬂows to

China. After that, we ranked the nodes in the

network from the highest to the lowest based

on the results degree calculation (Table 1).

According to Table 1, the ﬁrst eight nodes

{rdr,RDr,RDd,RrD,rrd,DDR,drr,RDR}

have highest rank. The summed degree of

these nodes is 55.56%, and the degree of any

of these 8 nodes is more than 3% greater

than that of the others in the network of

inbound tourist ﬂows, that is, 28.57% of the

nodes represent 55.56% of the degrees of the

network. This property means that these ﬂuc-

tuation patterns have a signiﬁcant role in

shaping macroscopic patterns of variations in

inbound tourist ﬂows and in inﬂuencing

other patterns. In the process of transform-

ation of the ﬂuctuation patterns, more trans-

formations should use these patterns as an

intermediate step. Identifying the out-degree

of nodes in the network of inbound tourist

ﬂows contributes to understanding the ﬂuctu-

ation rule and to forecasting future change.

For example, the ﬂuctuation pattern RDd can

transform into three other types of patterns:

RrD,Rrd,andRdd. The transformation prob-

abilities are 0.57, 0.29, and 0.14, respectively.

The transformation probability between RDd

and RrD is greater than the other transform-

ation probabilities. The double-logarithmic

degree distribution and cumulative degree dis-

tribution plot of the network of inbound

tourist ﬂows to China (Figure 3) shows few

nodes with a high degree value. Most of the

nodes are of lower degree value. Overall, the

degree distribution of the network of inbound

Table 1 Degree of Nodes in the Network of Inbound Tourist Flows to China

Node rdr RDr RDd RrD rrd DDR drr RDR ··· dDr

Degree 9 7 7 7 6 6 4 4 ··· 1

Rank 1 2 2 2 5 5 7 8 ··· 28

948 Yongrui Guo et al.

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tourist ﬂows to China follows a power-law dis-

tribution. Thus, only a handful of ﬂuctuation

patterns signiﬁcantly inﬂuence the ﬂuctuations

in the inbound tourist ﬂows to China.

Transformation Intermediary

In the transition process governing the ﬂuctu-

ation patterns, we focus on the types of ﬂuctu-

ation patterns that play an intermediary role in

the transformations. Thus, we can analyze the

betweenness centrality (BC) for each ﬂuctu-

ation pattern in the network of inbound

tourist ﬂows. In network theory, the between-

ness centrality of node vis the number of paths

from all nodes (except v) to all other nodes

that must pass through node v. The between-

ness centrality measures the intermediary or

middleperson power of a node. The between-

ness centrality of a node indicates its capability

to obtain and control resources or infor-

mation. Nodes with a high betweenness cen-

trality may have considerable inﬂuence

within a network by virtue of their control

over information or resources passing

between other nodes. The betweenness cen-

trality of a node vis given by the following

expression:

gv=

{i,j}

cij(v)

cij

,(5)

where g

v

is the betweenness centrality of a

node v,c

ij

is the total number of shortest

paths from node ito node j, and c

ij

(v) is the

number of those paths that pass through v.

The length of a path is the sum of the

weights of edges between iand j. The between-

ness centrality reveals the topological impor-

tance of nodes in its role in the transmission

of network information between each pair of

nodes. Therefore, the betweenness centrality

of a speciﬁc node can be explained as its

network inﬂuence. In the network of

inbound tourist ﬂows, the network inﬂuence

of a speciﬁc node is the power of a ﬂuctuation

pattern of inbound tourist ﬂows to control or

affect other patterns in the network.

The betweenness centrality of the nodes in

the network of inbound tourist ﬂows is

shown in Table 2. The differences among

nodes in betweenness centrality are evident.

The summed betweenness centrality of the

ﬁrst 8 nodes is 63.18%, and the betweenness

centrality of any of these 8 nodes is more

Figure 3 Degree Distribution (a) and Cumulative Degree Distribution (b) in the Network of

Inbound Tourist Flows to China.

Modeling the Fluctuations of Tourist Flows 949

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than 3% greater than that of the others; that

is, 28.57% nodes represent 63.18% of the

betweenness centrality of the network.

According to the statistics, six of the ﬂuctu-

ation patterns {rdr,RDr,RDd,RrD,rrd,

DDR}listed in the top eight in degree rank

remain on the list in betweenness centrality.

This result means that these ﬂuctuation pat-

terns are important intermediaries in the trans-

formation process for the ﬂuctuation patterns

of inbound tourist ﬂows. To a certain extent,

these ﬂuctuation patterns can serve as a

precursor to the transformations between pat-

terns. These nodes are helpful in understand-

ing the inherent laws and transformation

information of the ﬂuctuations in inbound

tourist ﬂows to China. Furthermore, signiﬁ-

cant differences among the betweenness cen-

trality of the nodes also suggest the presence

of higher volatility in the inbound tourist

ﬂows to China.

Transformation Distance

Studying the shortest path length of the

network of inbound tourist ﬂows can help us

understand the transition distance between

ﬂuctuation patterns. The shortest path is the

minimum number of edges needed to connect

any two nodes. The average shortest path of

network Lis the average value of the shortest

path lengths of all of the connections between

two nodes, and it is deﬁned as

L=2

N(N−1)

i≥j

dij,(6)

where d

ij

is the distance between nodes iand j

and Nis the total number of nodes in the

network. As shown in Table 3, the shortest dis-

tance and the longest distance between nodes

are 1 and 8, respectively. The most frequentdis-

tances, 3 and 4, represent more than 54% of the

cases in the network of inbound tourist ﬂows.

The calculated value of the average shortest

path is 3.38. Therefore, if one type of ﬂuctuation

pattern transforms into another, it will basically

change via three or four types of patterns.

Different types of ﬂuctuation patterns rarely

Table 2 Betweenness Centrality of Nodes in the Network of Inbound Tourist Flows to China

Vertex rdr RDr RrD DDR DdR RDd rrd rDr ··· DdD

BC/% 14.71 11.53 7.46 7.45 6.81 6.75 4.65 3.78 ··· 0.32

Rank 1 2 3 4 5 6 7 8 ··· 28

Table 3 Frequencies of Shortest Path

Distances in the Network of Inbound Tourist

Flows to China

Distance Frequency Proportion (%)

1 60 7.9

2 138 18.3

3 213 28.2

4 199 26.3

5 100 13.2

6 36 4.8

7 9 1.2

8 1 0.1

950 Yongrui Guo et al.

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transform into each other directly (distance of 1,

which accounts for 7.9% of cases). In the longest

path of transformation, a type of ﬂuctuation

pattern transforms via 8 types of patterns, but

this case is infrequent (0.1% of cases). A trans-

formation occurred approximately every three

to four quarters. This information is used as a

basis for predicting changes in inbound tourist

ﬂows in the next year. The results of the analysis

demonstrate that the transformations between

ﬂuctuation patterns of inbound tourist ﬂows

occur frequently.

Conclusions

This paper analyzed the ﬂuctuation patterns of

monthly inbound tourist ﬂows to China from

January 1990 to December 2012 using a

complex network approach. We constructed

a weighted network of inbound tourist ﬂows

to China. The nodes represent 28 ﬂuctuation

patterns of inbound tourist ﬂows to China,

the edges are the transformations between

nodes, and the weight of an edge is the

number of transformations between the two

types of ﬂuctuation patterns.

The most important nodes in the network are

rdr,RDr,RDd,RrD,rrd, and DDR. The

degree and betweenness of these nodes are

greater than those of other nodes in the

network of inbound tourist ﬂows. The

summed degree and betweenness of these

nodes reach values of 46.67% and 52.58%,

respectively. In the process of transformation

of ﬂuctuation patterns, more transformations

should use these patterns as an intermediate

step. We can identify signiﬁcant ﬂuctuation

patterns of inbound tourist ﬂows using these

topologically important nodes in the network.

These signiﬁcant ﬂuctuation patterns of

inbound tourist ﬂows play a key role in

pattern transformation and can be viewed as

the prelude to changes in inbound tourist

ﬂows. These ﬂuctuation patterns are helpful

in understanding the inherent laws and trans-

formation information related to the ﬂuctu-

ation in inbound tourist ﬂows to China. The

average transition distance was 3.38, and a

transformation occurred approximately every

3–4 quarters. These results demonstrate that

the transformations between ﬂuctuation pat-

terns of inbound tourist ﬂows occur frequently.

This paper analyzed the complex character-

istics of the ﬂuctuation patterns of monthly

inbound tourist ﬂows to China from the perspec-

tive of network topology. This method was of

guiding signiﬁcance in identifying the important

ﬂuctuation patterns and understanding the

inherent laws of the ﬂuctuations in tourist

ﬂows. The statistical properties of ﬂuctuations

in tourist ﬂows are important for modeling the

complex dynamics of tourist ﬂows and are of

great signiﬁcance for practical applications such

as tourist ﬂow risk estimation and tourism ﬂow

forecasting. According to this method and the

results in this paper, a forecasting model can be

built using the transformation intermediary, the

transformation probability and the transform-

ation time. This model differs from previous

tourism demand forecasting models because the

model is based on the ﬂuctuation patterns of

tourist ﬂows but not on the time series itself.

This difference is a direction for future research.

Acknowledgement

This work was supported by the National

Natural Science Foundation of China (Grant

No. 41171121, 41301134).

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