A Network Evolution Model for Chinese Traditional Acquaintance Networks
S NU ES T W
A IONRAKB LE IVTOY L U T I O N M O D E L S
A Network
Evolution Model for
Chinese Traditional
Acquaintance
Networks
Xi Chen, Lan Zhang, and Wei Li, Huazhong University of Science and Technology
A model of
S
Chinese traditional
mainly investigate topological features and evolution mechanisms from data—
acquaintance
for example, for viral marketing and email filtering via social networks.1
relationship
networks that
emphasizes
individual
heterogeneity
and social culture
incorporates three
distinct mechanisms
that affect network
evolution and
formation: heredity
linking, variation
linking, and
similarity-based
disconnection.
SEPTEMBER/OCTOBER 2014
ocial networks have attracted a great deal of interest from researchers in different scientific fields. Existing applications of social networks
Indeed, little attention is paid to offline social relationships. The technique of link
prediction from a constructivist view has
helped users make implicit connections
through online websites with those of similar interests. 2 With respect to acquaintance
relationships, the general method of how to
represent the processes and results of relation formation in real life remain unclear.
Such networks are conceived by researchers
as a crucial way for people to exchange information and spread public opinion.
It’s widely accepted that acquaintance
networks are small-world networks with
large clustering coefficients and scale-free
features. Many network evolution models that correspond well to features of
social networks in real life have been proposed.3-7 Jörn Davidson and his colleagues5
proposed an acquaintance network model
based on two rules—one for introductions
and by-chance meetings, and one for the
effects of aging on acquaintance networks.
Based on this model, friendship formation transaction costs and retention costs
were considered for improvement in ChungYuan Huang and Yu-Shiuan Tsai’s model. 6
Marián Boguñá and his colleagues7 studied a class of acquaintance network models
based on distance attachment. To explain
the nature of the structure of acquaintance
networks, dynamic evolution mechanisms
for generating specific network features
have been explored—for example, a rewiring mechanism has been found to lie in
small-world networks, 8 and preferential attachment becomes an important common
rule in networks with power-law degree
distribution.9 Other mechanisms, including
the fit-get-richer and transitive linking, have
been developed to drive dynamical network
evolution.
For the study of interpersonal relations, Mark S. Granovetter proposed two
1541-1672/14/$31.00 © 2014 IEEE
Published by the IEEE Computer Society
5
NETWORK EVOLUTION MODELS
definitions: strong ties and weak
ties.10 This theory, however, inadequately applies to the Chinese case
due to the specific forms of Chinese acquaintance communication.
Guanxi is proposed as an essential
element of everyday social life that
infiltrates every aspect of Chinese society. Deeply embedded in Chinese
culture, with a history of more than
5,000 years,11,12 Guanxi refers to the
concept of drawing on a web of connections to secure favors in personal
and organizational relations. Xiaotong Fei13 pointed out that China is
a relationship-based society with a
multilayer networked structure. This
famous theory laid the foundation
for research on Chinese Guanxi. According to Fei, Chinese traditional
acquaintance relationships are built
with close family members at the
core and distant relatives, classmates,
and friends arranged on the periphery according to the distance of the
relationship and the degree of trust.
Family principle,14 where the family is the basis of society, is perhaps
more true of China than of any other
highly developed nation. Acquaintance communication depends on the
natural “blood” and geographic relationships that are characteristic of
the Chinese special kinship culture.
Generations of deeply rooted individuals are the normal state of society. Isolation, however, is also present
between different communities as individuals survive on their own in a
vast rural area. Consequently, the acquaintance communication under a
Chinese cultural environment is different from other types of societies.
Previously developed acquaintance
network models have shown the existence of small-world properties
and scale-free features, but they assume that nodes are the same and fail
to take different social cultures into
account. In this study, we incorporate
6
three new mechanisms—heredity
linking, variation linking, and similarity-based disconnection—to form
an evolution model of the Chinese
acquaintance relationship network.
Combined with actual statistical
birth and death rate data, our numerical results not only show small-world
characteristics but also imply the native characteristics of a Guanxicentered society that are absent in
other models of social networks.
Topological Features of
Acquaintance Networks
To put forward our model of acquaintance networks, we must first
detail the related definitions that play
key roles in the evolution process.
Attributes of Individuals
In previous studies of acquaintance
network modeling, the heterogeneity
of individuals wasn’t given, and individuals in social networks were assumed to be identical. But obviously,
different social individuals manifest
different social attributes and preferences to acquaint themselves with
others. In our model, five basic attributes forming an attribute set
represent the heterogeneity among individuals. Specifically, attribute sets
of individual (node) i contain the following attributes:
• agei is a nonnegative integer representing node i’s age;
• genderi is specified as male or female according to node i’s gender;
• edui is an assignment for education level of node i—it’s quantified
as a float number between 0 and 1,
where 0 stands for the lowest education level (illiteracy) and 1 stands
for the highest education level;
• ecoi denotes the economic level of
the area node i is in—it’s quantified
by a float number between 0 and
1, where 1 denotes an economic
www.computer.org/intelligent
condition at its most developed;
and
• gpxi and gpyi represent latitude and
longitude of node i, respectively.
Next, we consider how to calculate
similarity.
Similarity
Various approaches, such as cosine
similarity measure, have been proposed to calculate the similarity
between users in collaborative recommender systems. With respect to
our acquaintance networks, similarity is defined as the attraction degree
among people. Acquaintance communication shows that you’re more
likely to establish or maintain a social contact if you have a high degree
of similarity.
Similarity between node i and node
j (Sij) is computed based on individual
attribute vectors. According to different types of value, Sij is categorized
into identical similarity ( S1ij ), degree
similarity ( Sij2 ), and reverse similarity ( Sij3).
For identical similarity, S1ij is defined for attributes with only two values. Here, only gender is included. S1ij
is quantified as
0 ,
S1ij =
1 ,
if genderi ≠ genderj
if genderi = genderj .
For degree similarity, Sij2 is defined
in terms of the attribute with a float
number. Here, age similarity ( Sijage ),
education similarity ( Sijedu ), and economy similarity ( Sijeco ) are included.
age
Sij is measured as
age
Sij
= 1−
agei − age j
max {agei ,age j }
,
Sijedu and economy Sijeco are calculated in
the same way. Then, Sij2 is summed as
age
Sij2 = [ w age , w edu , w eco ] ⋅ [ Sij , Sijedu , Sijeco ]T ,
IEEE INTELLIGENT SYSTEMS
where w age , w edu, and w eco are the
weights of age, education, and economy specified by experts.
For reverse similarity, Sij3 measures
geographical position and is inversely
proportional to distance between two
nodes, based on the Hamming distance. Sij3 is computed as
Sij3 = 1 −
(gpx i − gpx j )2 + (gpy i − gpy j )2
dmax
,
where dmax is the maximum distance
among all nodes.
By combining S1ij , Sij2, and Sij3, Sij is
computed as
Sij = [ w1 , w 2 , w3 ] ⋅ [ S1ij , Sij2 , Sij3 ]T ,
where w 1, w 2 , and w 3 are the weights
of each kind of similarity specified by
experts. For convenience of calculation, the values of similarity are normalized between [0, 1].
Heredity and Variation
Inspired by Darwinian evolution and
Chinese special kinship culture, we
think of the formation and evolution of
acquaintance relationships as following the ideas of heredity and variation.
In Chinese traditional rural society, social relationship structure is
dominated by extreme particularism.
Blood/geographical relations are basic social relations attached to traditional people. The clansman trust in
each other and the patriarchal clan
structure makes groups more unified.
People become acquainted with their
relatives at a much higher probability than strangers—that is, most acquaintance network relationships are
naturally inherited from family and
irrelevant to an individual’s attributes.
This kinship, resulting from marriage
and procreation, is the most pervasive relationship in Chinese society.
Each person has a kinship network,
SEPTEMBER/OCTOBER 2014
and social relationships spread out
through many personal relations. We
define heredity linking as the process
of relationship formation; friendship
recommendation means that you’re
more likely to make friends through
acquaintances. We assume that the
central mechanism of the dynamics
of acquaintance networks is that people are introduced to each other by a
common acquaintance.
People generally tend to associate with family members. Only when
the family group can’t meet the demand will they consider associating
and forming relations with strangers. In some cases, people become
acquainted based on occupational
relations or other common characteristics. Variation is developed into
our acquaintance model to describe
such tendencies. Acquaintanceship is
generally influenced by individual social attributes, which means that you
have higher linking probability to another person due to high similarity,
adhering to preferential attachment.
Fitness
A fitness parameter is defined to measure different individual abilities for
environmental adaptation, which affects the process of making connections with others. Fi is assigned to
node i to denote the fitness of node i.
It’s quantified as a float number between 0 and 1, where 1 stands for the
maximum fitness value. Because the
fitness of most people is around the
average value, and individuals with
extremely large or small fitness are relatively uncommon, random numbers
are generated between [0, 1] according
to the (0.5, 0.012) normal distribution
as the initial fitness for each node.
An Evolution Model for
Acquaintance Networks
Now that we’ve covered the basic
terms, we can construct an evolution
www.computer.org/intelligent
model for Chinese traditional acquaintance networks appropriate for China’s specific social context. But first,
we must give a description of some assumptions pertaining to the model:
• According to Chinese law, an individual over 16 years old is sexually
mature and has reached the age of
consent. Taking individual cognition into consideration, it’s assumed that individuals over 16
years old have the ability of heredity and variation.
• Because individual resources and
friend-making costs are finite,
there’s an upper limit on the number of friendships an individual can
maintain.
• The number of nodes dynamically
changes based on birth and death
rate statistics.
Now, let’s look at our generation
algorithm.
Generation Algorithm
Acquaintance networks evolve as new
acquaintances form, old friendships
dissolve, and people join and leave
networks. New rules should consider
how individuals connect or disconnect with others in Chinese society.
Figure 1 shows a simulated flowchart
of our proposed model.
Our model operates as follows. Step
1 covers parameter initialization. According to statistical proportion, essential data is generated to initialize
the five basic attributes of each node.
This step assigns an initial fitness
value for each node and sets appropriate heredity and variation linking
proportions.
During Step 2, the network construction stage, an original network
is formulated with an initial number of N nodes and undirected edges
between pairs of nodes according to
network parameters.
7
NETWORK EVOLUTION MODELS
Start
Parameter initialization
Birth
Network construction
Size of nodes
Death
Evolution rules
N
Heredity linking
Size of connections
Variation linking
Stationary?
Similarity-based
disconnection
Y
End
Figure 1. Acquaintance network model flowchart. Step 1 is parameter initialization,
Step 2 is network construction, Step 3 is network evolution, and in Step 4 the
evolution is complete.
Step 3 handles network evolution.
During each time step, the size of
nodes and the scale of connections
both undergo variable change. The
dynamics of the model consist of the
following processes taking place at
each time step:
• Birth and death. According to each
year’s birth rate, new nodes arrive
and their attributes are initialized.
Old vertices are removed from the
acquaintance network at the year’s
death rate according to census data.
• Heredity and variation linking. Heredity linking and variation linking
are two dominant behaviors during
evolution.
• Similarity-based
disconnection.
Disconnection based on similarity denotes the social reality that
relationships are hard to maintain
between individuals with great
differences. Because the contacts
an individual can manipulate are
finite, if new acquaintances form
continually, an individual with
excessive degrees of connections
will break connections with some
8
acquaintances selectively. Disconnection based on minimum similarity is designed here to balance
the individual relation. It means
one randomly chosen node i will
remove the associated edge with
neighbor node j according to the
disconnection probability ( pijd ),
which is inversely proportional to
similarity as
pijd = 1 −
Sij
∑ Sil
,
l ∈ Li
where Li denotes the node collection of node i’s neighbors.
In Step 4, the evolution is completed. The simulation is over when
the simulation time comes to an end
or the network topological features
all achieves stationary states. If not,
the model jumps back to Step 3 and
continues the evolution process.
Heredity Linking
In the Chinese Guanxi-centered cultural environment, acquaintancewww.computer.org/intelligent
forming mainly derives from heredity
linking, which means a preference in
choice for neighbors of friends (here,
friends mean relatives or family).
According to the scale-free network
model, a node with a bigger degree
has a higher probability of forming
connections. However, this isn’t completely accordant with the reality of
friendship formation. When choosing
partners and establishing new relations, the individual not only considers
the quantity of another individual’s relations (degree k), he or she also values
the ability of the person to adapt to the
environment (fitness). If a person has
strong fitness, although his group of
friends is small, many individuals will
choose to become acquaintances with
him. Consequently, the linking probability phl
j that a randomly chosen node
i will be connected to node j depends
on the fitness (Fj) and the degree (kj) of
node j, so that
p hl
j =
Fj × kj
∑ ( Fm × km ) ,
m∈Mi
where Mi denotes the neighbor collection of node i’s neighbors.
The dynamics of the heredity process is defined as follows:
1. Randomly choose a node i from
the acquaintance network.
2. If the degree of node i reaches the
maximum value, reselect a random node. Randomly pick node
j from the neighbor collection of
node i’s neighbors (Mi).
3. If a random float number generated by the (0, 1) uniform distribution is lower than probability
p hl
j , insert an edge between nodes
i and j. If the heredity linking
number has reached the proportion number, heredity linking is
completed; otherwise, execute
from the beginning repeatedly.
IEEE INTELLIGENT SYSTEMS
Table 1. Statistical data from the fifth population census of China.
Gender (%)
Male
51.63
Age (%)
Female
Infants
Child
Juvenile
48.37
3.17
5.08
14.67
Proportion of education among the juvenile (%)
Illiteracy
2.68
Youth
Middle-aged
Elderly
37.61
29.76
9.71
Proportion of education among the youth (%)
Primary
Intermediate
Senior
Illiteracy
75.79
21.53
0
2.04
Proportion of education among the middle-aged (%)
Primary
Intermediate
Senior
21.63
70.35
5.98
Proportion of education among the elderly (%)
Illiteracy
Primary
Intermediate
Senior
Illiteracy
Primary
Intermediate
Senior
8.88
38.26
49
3.86
47.55
36.82
13.58
2.05
The heredity linking number is the
result of the size of nodes and the heredity proportion.
Variation Linking
Variation linking models the tendency of individuals to associate with
others based on occupational relations; acquaintance relation formation occurs on the basis of individual
social attributes. Variation means
choosing connected individuals based
on similarities adhering to preferential attachment. Linking the probability between nodes i and j ( pijvl ) is
calculated as
pijvl =
Sij
∑ Siq
,
q ∈Qi
where Qi denotes the collection of
those outside of node i’s neighbors.
The dynamics of the variation process is defined as follows:
1. Randomly choose a node i from
the acquaintance network.
2. If the degree of node i reaches the
maximum value, reselect a random node. Randomly pick node j
from the collection of those outside of node i’s neighbors (Qi).
3. If a random float number generated by the (0, 1) uniform distribution is lower than probability pijvl ,
insert an edge between node i and
j. If variation linking number has
reached the proportion number,
variation linking is completed;
SEPTEMBER/OCTOBER 2014
otherwise, execute from the beginning repeatedly.
The variation linking number is
jointly determined by the size of
nodes and variation proportion.
distribution as each node’s initial fitness. In this way, the probability that
RF exceeds 1 is larger, about 60 percent, indicating that individual fitness, compared to decrease, increases
with a higher probability. If it is above
1, Fi∗ will be set to 1.
Fitness Update Law
During the network evolution process,
the fitness of an individual dynamically changes as he or she establishes
new relations or loses contact with
others. The fitness update law is based
on the Matthew effect, which states
that an individual with strong fitness
will obtain stronger fitness and one
with weak fitness will obtain weaker
fitness. Thus, the updated fitness of
node i (Fi∗) is computed by
Fi∗ = λ × Fi + (1 − λ ) × RF × Fi ,
where l is a correction factor. To
avoid excessive numerical value correction, let l = 0.8, where RF is a
modified index. When individual fitness F is lower than the mean value
0.5, RF is a random number generated between [0, 1] according to the
(0.9995, 0.000592) normal distribution as each node’s initial fitness. In
this way, the probability that RF is
lower than 1 is larger, about 60 percent, indicating that individual fitness, compared to increase, decreases
with a higher probability. On the contrary, when individual fitness is larger
than the mean value 0.5, the value of
RF is generated between [0, 1] according to the (1.000 5, 0.000592) normal
www.computer.org/intelligent
Numerical Results
Using the fifth population census data
for China, this article uses the statistical data of gender proportion, age
proportion, population proportion in
different geographical positions, and
education-level proportion, respectively, in juvenile, youth, middle age,
and old age. We obtain the economic
condition in different regions as well.
Table 1 shows gender, age, and education proportions.
The simulation environment is designed as follows:
• Essential data of 5,000 nodes’ attributes is generated according to
the statistical proportion of the
fifth national census.
• Initial network is a random network with 5,000 nodes and connections per node set as four.
• The platform for essential data
generation is developed in C#. The
simulation environment is Anylogic
6.0, and the database is SQLServer
2008.
• The acquaintance network evolves
with a month time step.
Now, let’s look at how various parameters influence acquaintance networks.
9
NETWORK EVOLUTION MODELS
25
5.5
Weak effect
Medium effect
Strong effect
20
L
5.00
155
4.55
100
4.00
0
2
4
6
8
5
10
0
2
Time step (x 4 years)
4
6
8
10
Time step (x 4 years)
(a)
(b)
10–1
0.2
0.15
P(k)
10–22
C
0.1
10–33
0.05
0
0
(c)
2
4
6
8
Time step (x 4 years)
10
10–44
100
(d)
101
102
103
k
Figure 2. Comparison among the topological features for a Chinese traditional acquaintance network with a weak, medium,
and strong effect of Guanxi. (a) Average path length with time. (b) Average degree with time. (c) Clustering coefficient with
time. (d) Degree distribution.
Parameter Analyses: Effects
of Heredity Proportion
To determine the effects of heredity and variation on acquaintance
networks, we first define weak, medium, and strong effects of Guanxi
with parameters initialized at different levels of heredity proportion—10
percent, 20 percent, and 30 percent,
respectively—with a fixed variation
proportion of 5 percent, and then
run a series of simulations. Figure 2
shows that each of the four properties
10
eventually converges to an asymptotic stable value with the same trend.
Simulation results show a low degree
of separation and a high degree of
clustering, characteristic of the smallworld properties of social networks.
Under the weak effect of Guanxi,
topological features of the acquaintance networks change slowly, but
the average degree can rise to a stable
value rapidly with a strong effect of
Guanxi. Because of the inheritance of
relations in Chinese society, a person
www.computer.org/intelligent
can make acquaintances quickly.
Consequently, the parameters of a
strong effect of Guanxi are selected
as the best values.
Model Validation and Discussion
To validate our acquaintance network evolution model, we contrast
our simulation with the simulation
results of Davidsen’s model 5 for N =
5,000 and p = 0.0025 and Huang’s
model6 for N = 5,000, p = 0.0025, b =
0.0001, f 0 = beta 14(0.5), q = 0.1,
IEEE INTELLIGENT SYSTEMS
Davidsen’s
Huang’s
CTAN
L
5.0
4.5
4.0
3.5
0
2
4
6
Time step
8
10
(a)
30
0.6
25
0.5
20
0.4
15
0.3
C
5.5
10
0.2
5
0.1
0
0
0
2
4
6
Time step
8
0
10
2
8
4
6
Time step
10
(c)
(b)
Figure 3. Comparison of topological features for Chinese traditional acquaintance network (CTAN), Davidsen’s network, and
Huang’s network. One time step in CTAN stands for four years; in Davidsen’s network and Huang’s network, it stands for
10,000 steps. (a) Average path length with time. (b) Average degree with time. (c) Clustering coefficient with time.
SEPTEMBER/OCTOBER 2014
100
2
Population proportion
38.06%
8.84%
52.02%
10–1
P(k)
q = 0.4, r = 1.0, b = 0.0001, which
is the best match for actual social activity scenarios according to the two
literatures.
Figure 3 presents the contrasting
result of average degree, clustering
coefficient, and average path length
with respect to time. From the result, it can be seen that the variation
trend of topological features of our
network is similar to the features of
Davidsen’s network. They both share
fluctuations, but there are differences
among the stable values of the three
metrics. The average degree of our
network can be stabilized in a shorter
time than Davidsen’s network. This
can be explained by the phenomenon
in Chinese rural society wherein close
relatives can be inherited from families quickly as stable acquaintance relationships. Comparatively speaking,
developed Western countries don’t
depend so heavily on kinship to facilitate interpersonal communication.
However, average path length in our
acquaintance network is longer than
in Davidsen’s, and the clustering coefficient in our acquaintance network
is lower than both Davidsen’s network and Huang’s network. We postulate that the corresponding social
phenomenon for this data is the normal existence of multigenerational
settled groups of individuals in the
Davidsen’s
Huang’s
CTAN
Power-law distribution
with an exponential cutoff
Exponential distribution
10–2
3
1
10–3
Population proportion
16.24%
0.38%
11.82%
Population proportion
45.7%
90.78%
36.16%
10–4
100
101
k
102
Figure 4. Comparison of the degree distribution for a Chinese traditional
acquaintance network (CTAN), Davidsen’s network, and Huang’s network. The
population proportions of the three networks in each segmentation are presented.
vast Chinese rural areas. Only a few
individuals are in contact with communities outside the kinship area.
Isolation characterizes the typical
relationship between these different
communities. Due to the third rule of
friendship updates in Huang’s model,
a large number of relations are disconnected, leading to a decrease in
www.computer.org/intelligent
the average degree and higher average
path length compared to the other
two networks.
Figure 4 shows the degree distribution of acquaintance networks
using the three models. According
to the degree distribution characteristics, we divided the population
proportions of the three networks
11
NETWORK EVOLUTION MODELS
into three segmentations for discussion. In Segmentation I, with a small
number of degrees, the population
proportion of our network (36.16
percent) is lower than the other two
networks (45.7 percent and 90.78
percent), indicating that individuals with few relations are less prevalent than in the other two networks.
In a group with few social relations,
there’s only a small minority. In Segmentation II, with a medium number
of degrees, our network’s degree distribution shows a slow decline, while
those of the other two networks fall
rapidly. The population proportion
of our network (52.02 percent) is
higher in the middle than the other
two networks (38.06 percent and
8.84 percent). The results illustrate
that most individuals maintain some
medium number of connections
through the inheritance mechanism.
In Segmentation III, with a sufficiently high number of degrees, the
three networks’ degree distribution
shows an emergent tendency of rapid
decrease, indicating that people who
own large numbers of social relations represent a small portion of the
total. On the whole, degree distribution in Davidsen’s network exhibits
a power-law regime for small p, and
Huang’s model produces a distribution feature that mixes power-law
and exponential distribution types.
In Segmentations I and II, our network displays a power-law form
with an exponential cutoff: P(k) ∼
e −bk(k + c) −g , the fitting parameters
of which are b = 0.0371, c = 0.974,
and g = 0.1064. In Segmentation III,
it follows an exponential distribution: P(k) ∼ le −lk, the parameter of
which is l = 0.0487.
Through comparative analysis, the
numerical results of our model provide valid explanations for some
widely accepted sociological conclusions pertaining to Chinese rural
12
society structure. Individuals with
relatively few relations in the Chinese hierarchical context are less
prominent than they are in Western societies, corresponding to Segmentation I. The implications of our
results support the view that the Chinese family is a tiny nation, shaping
its community by self-organization,
a familial rather than social integration noticed by American scholar
John King Fairbank.15 People with
medium degrees of relations in Segmentation II constitute the largest
proportion, an observation well explained in Fei’s classic conclusions.
Fei13 pointed out that, in China,
distribution of peak values in the
middle segmentation.
However, the opposing feature
of a large number of individuals in
Segmentation I in Western societies is due to group characteristics.
The Western acquaintance relationship is more equal and concise, and
can be conceived of as a metaphor,
the fasces, or sticks of wood bounded
together in parallel to each other. Individuals are independent, and acquaintance relationships don’t rely on
blood kinship. Taken as a whole, the
basic features in Chinese and Western society are totally different, and
the analysis of our network matches
well with the conclusions of sociological research.
The formation of
traditional acquaintance
relationships is greatly
affected by the special
Chinese kinship culture in
a Guanxi-centered society.
each person is part of a kinship network based on the axis of relatives.
Numerous kinship networks overlap
to form Chinese traditional acquaintance relationships. Compared with
Western countries, the Chinese traditional social structure is typically
an interpersonal interaction relationship network linked by blood, relative, and geographical relationships.
Kinship culture marks this acquaintance society more strongly than in
Western countries. As a result, individuals with medium relations constitute the largest proportion. The
characteristics of the Chinese acquaintance society in turn verify the
www.computer.org/intelligent
I
n this article, we introduced a
model of a Chinese traditional acquaintance network. In contrast to
previous acquaintance network models, we emphasize individual heterogeneity and social culture, and
incorporate three distinct mechanisms that result in acquaintance relationship formation and separation,
respectively: heredity linking, variation linking, and similarity-based
disconnection. Compared with the
acquaintance networks in Western
countries, our network shows irregular characteristics. The degree
distribution of Chinese traditional
acquaintance networks is manifested
as a piecewise approximation that
combines a power-law form with
an exponential cutoff and distribution. Numerical results show that
individuals with few or many relations in a Chinese hierarchical system are neither representative nor
especially prominent, and individuals whose degree is around the average value instead constitute the
largest proportion of the whole.
These results further indicate that the
IEEE INTELLIGENT SYSTEMS
THE AUTHORS
Xi Chen is an associate professor in the School of Automation at the Huazhong University of Science and Technology. His research interests include modeling and simulation,
agent and multiagent systems, emergency management, complex networks, artificial intelligence, and computational social science. Chen has a PhD in systems engineering from
the Huazhong University of Science and Technology. He’s a member of IEEE, a member
of the Artificial Intelligence Society of China, and a senior member of the Chinese Institute of Electronics. Contact him at chenxi@mail.hust.edu.cn.
Lan Zhang is a master’s student in the School of Automation at the Huazhong University of Science and Technology. Her research interests include social network modeling
and analysis, and multiagent systems. Zhang has a BS in systems engineering from the
Huazhong University of Science and Technology. Contact her at zhanglan1107@gmail.
com.
Wei Li is an associate professor in the School of Automation at the Huazhong University
of Science and Technology. Her research interests include modeling and simulation theory and application, complex systems science, intelligent control, and brain networks. Li
has a PhD in control science and engineering from the Huazhong University of Science
and Technology. She’s a member of IEEE and the Artificial Intelligence Society of China.
Contact him at liwei0828@mail.hust.edu.cn.
formation of traditional acquaintance
relationships is greatly affected by the
special Chinese kinship culture in a
Guanxi-centered society. Our findings are supported by sociological
statistical conclusions and offer a rational explanation for the nature of
Chinese kinship networks.
Still, there are some issues requiring
further study to achieve a better understanding of the structure of complex social networks. For example,
the individual attributes studied are
incomplete, and the cultural elements
considered are only partially representative of a real, complex society.
How different attributes affect network topology remains an interesting
topic for extensive study in the near
future.
Our work provides an adequate
framework for further research on
dynamic and complex human behaviors, such as epidemics spreading or rumors propagating. The
effect of network topology on information diffusion can be further explored in specified social networks.
Ultimately, our work contributes to
a greater emphasis on cultural diversity as a basic consideration for modeling more accurate acquaintance
networks.
SEPTEMBER/OCTOBER 2014
Acknowledgments
This work was supported by the National
Natural Science Foundation of China
(grant NSFC 70903026), the Fundamental
Research Funds for the Central Universities (HUST:2013TS125), and the Key Laboratory of Ministry of Education for Image
Processing and Intelligent Control, China.
We thank Xiaolei Yang for proving essential
data and Qin Tu for developing the simulation platform. We’re grateful to those people
who provided useful reference articles and
contributed their valuable suggestions.
References
1. S. Staab et al., “Social Networks Applied,” IEEE Intelligent Systems, vol.
20, no. 1, 2005, pp. 80–93.
2. B. Bringmann et al., “Learning and
Predicting the Evolution of Social Networks,” IEEE Intelligent Systems, vol.
25, no. 4, 2010, pp. 26–35.
3. G. Bianconi and A. Barabási, “BoseEinstein Condensation in Complex
Networks,” Physical Rev. Letters, vol.
86, 2001, pp. 5632–5635.
4. E.M. Jin, M. Girvan, and M.E.J. Newman, “Structure of Growing Social
Networks,” Physical Rev. E, vol.
64, no. 046132, 2001; http://dx.doi.
org/10.1103/PhysRevE.64.046132.
5. J. Davidsen, H. Ebel, and S. Bornholdt,
“Emergence of a Small World from
Local Interactions: Modeling Acquaintance Networks,” Physical Rev. Letters,
www.computer.org/intelligent
vol. 88, no. 12, 2002; http://dx.doi.
org/10.1103/PhysRevLett.88.128701.
6. C.Y. Huang and Y.S. Tsai, “Effects
of Friend-Making Resources Costs
and Remembering on Acquaintance
Networks,” Physica A, vol. 389, no. 3,
2010, pp. 604–622.
7. M. Boguñá et al., “Models of Social
Networks Based on Social Distance
Attachment,” Physical Rev. E, vol. 70,
no. 056122, 2004, doi:10.1103/
PhysRevE.70.056122.
8. D.J. Watts and S.H. Strogatz, “Collective Dynamics of ‘Small World’
Networks,” Nature, vol. 393, 1998, pp.
440–442; doi:10.1038/30918.
9. R. Albert and A.L. Barabasi, “Emergence of Scaling in Random Networks,”
Science, vol. 286, no. 5439, 1999, pp.
509–512.
10. M.S. Granovetter, “The Strength of
Weak Ties,” Am. J. Sociology, vol. 78,
no. 6, 1973, pp. 1360–1380.
11. S.H. Park and Y. Luo, “Guanxi and
Organizational Dynamics: Organizational Networking in Chinese Firms,”
Strategy Management J., vol. 22, 2001,
pp. 455–477.
12. X.P. Chen and C. Chen, “On the Intricacies of the Chinese Guanxi: A Process
Model of Guanxi Development,” Asia
Pacific J. Management, vol. 21, 2004,
pp. 305–324.
13. X.T. Fei, From the Soil: The Foundations of Chinese Society, Peking Univ.
Press, 1998 (in Chinese).
14. X. Zhai, “Trait of Chinese Interpersonal Relationship,” Sociological Research,
vol. 4, 1993, pp. 74–83 (in Chinese).
15. J.K. Fairbank, The United States and
China, Harvard Univ. Press, 1948.
Selected CS articles and columns
are also available for free at
http://ComputingNow.computer.org.
13
A IONRAKB LE IVTOY L U T I O N M O D E L S
A Network
Evolution Model for
Chinese Traditional
Acquaintance
Networks
Xi Chen, Lan Zhang, and Wei Li, Huazhong University of Science and Technology
A model of
S
Chinese traditional
mainly investigate topological features and evolution mechanisms from data—
acquaintance
for example, for viral marketing and email filtering via social networks.1
relationship
networks that
emphasizes
individual
heterogeneity
and social culture
incorporates three
distinct mechanisms
that affect network
evolution and
formation: heredity
linking, variation
linking, and
similarity-based
disconnection.
SEPTEMBER/OCTOBER 2014
ocial networks have attracted a great deal of interest from researchers in different scientific fields. Existing applications of social networks
Indeed, little attention is paid to offline social relationships. The technique of link
prediction from a constructivist view has
helped users make implicit connections
through online websites with those of similar interests. 2 With respect to acquaintance
relationships, the general method of how to
represent the processes and results of relation formation in real life remain unclear.
Such networks are conceived by researchers
as a crucial way for people to exchange information and spread public opinion.
It’s widely accepted that acquaintance
networks are small-world networks with
large clustering coefficients and scale-free
features. Many network evolution models that correspond well to features of
social networks in real life have been proposed.3-7 Jörn Davidson and his colleagues5
proposed an acquaintance network model
based on two rules—one for introductions
and by-chance meetings, and one for the
effects of aging on acquaintance networks.
Based on this model, friendship formation transaction costs and retention costs
were considered for improvement in ChungYuan Huang and Yu-Shiuan Tsai’s model. 6
Marián Boguñá and his colleagues7 studied a class of acquaintance network models
based on distance attachment. To explain
the nature of the structure of acquaintance
networks, dynamic evolution mechanisms
for generating specific network features
have been explored—for example, a rewiring mechanism has been found to lie in
small-world networks, 8 and preferential attachment becomes an important common
rule in networks with power-law degree
distribution.9 Other mechanisms, including
the fit-get-richer and transitive linking, have
been developed to drive dynamical network
evolution.
For the study of interpersonal relations, Mark S. Granovetter proposed two
1541-1672/14/$31.00 © 2014 IEEE
Published by the IEEE Computer Society
5
NETWORK EVOLUTION MODELS
definitions: strong ties and weak
ties.10 This theory, however, inadequately applies to the Chinese case
due to the specific forms of Chinese acquaintance communication.
Guanxi is proposed as an essential
element of everyday social life that
infiltrates every aspect of Chinese society. Deeply embedded in Chinese
culture, with a history of more than
5,000 years,11,12 Guanxi refers to the
concept of drawing on a web of connections to secure favors in personal
and organizational relations. Xiaotong Fei13 pointed out that China is
a relationship-based society with a
multilayer networked structure. This
famous theory laid the foundation
for research on Chinese Guanxi. According to Fei, Chinese traditional
acquaintance relationships are built
with close family members at the
core and distant relatives, classmates,
and friends arranged on the periphery according to the distance of the
relationship and the degree of trust.
Family principle,14 where the family is the basis of society, is perhaps
more true of China than of any other
highly developed nation. Acquaintance communication depends on the
natural “blood” and geographic relationships that are characteristic of
the Chinese special kinship culture.
Generations of deeply rooted individuals are the normal state of society. Isolation, however, is also present
between different communities as individuals survive on their own in a
vast rural area. Consequently, the acquaintance communication under a
Chinese cultural environment is different from other types of societies.
Previously developed acquaintance
network models have shown the existence of small-world properties
and scale-free features, but they assume that nodes are the same and fail
to take different social cultures into
account. In this study, we incorporate
6
three new mechanisms—heredity
linking, variation linking, and similarity-based disconnection—to form
an evolution model of the Chinese
acquaintance relationship network.
Combined with actual statistical
birth and death rate data, our numerical results not only show small-world
characteristics but also imply the native characteristics of a Guanxicentered society that are absent in
other models of social networks.
Topological Features of
Acquaintance Networks
To put forward our model of acquaintance networks, we must first
detail the related definitions that play
key roles in the evolution process.
Attributes of Individuals
In previous studies of acquaintance
network modeling, the heterogeneity
of individuals wasn’t given, and individuals in social networks were assumed to be identical. But obviously,
different social individuals manifest
different social attributes and preferences to acquaint themselves with
others. In our model, five basic attributes forming an attribute set
represent the heterogeneity among individuals. Specifically, attribute sets
of individual (node) i contain the following attributes:
• agei is a nonnegative integer representing node i’s age;
• genderi is specified as male or female according to node i’s gender;
• edui is an assignment for education level of node i—it’s quantified
as a float number between 0 and 1,
where 0 stands for the lowest education level (illiteracy) and 1 stands
for the highest education level;
• ecoi denotes the economic level of
the area node i is in—it’s quantified
by a float number between 0 and
1, where 1 denotes an economic
www.computer.org/intelligent
condition at its most developed;
and
• gpxi and gpyi represent latitude and
longitude of node i, respectively.
Next, we consider how to calculate
similarity.
Similarity
Various approaches, such as cosine
similarity measure, have been proposed to calculate the similarity
between users in collaborative recommender systems. With respect to
our acquaintance networks, similarity is defined as the attraction degree
among people. Acquaintance communication shows that you’re more
likely to establish or maintain a social contact if you have a high degree
of similarity.
Similarity between node i and node
j (Sij) is computed based on individual
attribute vectors. According to different types of value, Sij is categorized
into identical similarity ( S1ij ), degree
similarity ( Sij2 ), and reverse similarity ( Sij3).
For identical similarity, S1ij is defined for attributes with only two values. Here, only gender is included. S1ij
is quantified as
0 ,
S1ij =
1 ,
if genderi ≠ genderj
if genderi = genderj .
For degree similarity, Sij2 is defined
in terms of the attribute with a float
number. Here, age similarity ( Sijage ),
education similarity ( Sijedu ), and economy similarity ( Sijeco ) are included.
age
Sij is measured as
age
Sij
= 1−
agei − age j
max {agei ,age j }
,
Sijedu and economy Sijeco are calculated in
the same way. Then, Sij2 is summed as
age
Sij2 = [ w age , w edu , w eco ] ⋅ [ Sij , Sijedu , Sijeco ]T ,
IEEE INTELLIGENT SYSTEMS
where w age , w edu, and w eco are the
weights of age, education, and economy specified by experts.
For reverse similarity, Sij3 measures
geographical position and is inversely
proportional to distance between two
nodes, based on the Hamming distance. Sij3 is computed as
Sij3 = 1 −
(gpx i − gpx j )2 + (gpy i − gpy j )2
dmax
,
where dmax is the maximum distance
among all nodes.
By combining S1ij , Sij2, and Sij3, Sij is
computed as
Sij = [ w1 , w 2 , w3 ] ⋅ [ S1ij , Sij2 , Sij3 ]T ,
where w 1, w 2 , and w 3 are the weights
of each kind of similarity specified by
experts. For convenience of calculation, the values of similarity are normalized between [0, 1].
Heredity and Variation
Inspired by Darwinian evolution and
Chinese special kinship culture, we
think of the formation and evolution of
acquaintance relationships as following the ideas of heredity and variation.
In Chinese traditional rural society, social relationship structure is
dominated by extreme particularism.
Blood/geographical relations are basic social relations attached to traditional people. The clansman trust in
each other and the patriarchal clan
structure makes groups more unified.
People become acquainted with their
relatives at a much higher probability than strangers—that is, most acquaintance network relationships are
naturally inherited from family and
irrelevant to an individual’s attributes.
This kinship, resulting from marriage
and procreation, is the most pervasive relationship in Chinese society.
Each person has a kinship network,
SEPTEMBER/OCTOBER 2014
and social relationships spread out
through many personal relations. We
define heredity linking as the process
of relationship formation; friendship
recommendation means that you’re
more likely to make friends through
acquaintances. We assume that the
central mechanism of the dynamics
of acquaintance networks is that people are introduced to each other by a
common acquaintance.
People generally tend to associate with family members. Only when
the family group can’t meet the demand will they consider associating
and forming relations with strangers. In some cases, people become
acquainted based on occupational
relations or other common characteristics. Variation is developed into
our acquaintance model to describe
such tendencies. Acquaintanceship is
generally influenced by individual social attributes, which means that you
have higher linking probability to another person due to high similarity,
adhering to preferential attachment.
Fitness
A fitness parameter is defined to measure different individual abilities for
environmental adaptation, which affects the process of making connections with others. Fi is assigned to
node i to denote the fitness of node i.
It’s quantified as a float number between 0 and 1, where 1 stands for the
maximum fitness value. Because the
fitness of most people is around the
average value, and individuals with
extremely large or small fitness are relatively uncommon, random numbers
are generated between [0, 1] according
to the (0.5, 0.012) normal distribution
as the initial fitness for each node.
An Evolution Model for
Acquaintance Networks
Now that we’ve covered the basic
terms, we can construct an evolution
www.computer.org/intelligent
model for Chinese traditional acquaintance networks appropriate for China’s specific social context. But first,
we must give a description of some assumptions pertaining to the model:
• According to Chinese law, an individual over 16 years old is sexually
mature and has reached the age of
consent. Taking individual cognition into consideration, it’s assumed that individuals over 16
years old have the ability of heredity and variation.
• Because individual resources and
friend-making costs are finite,
there’s an upper limit on the number of friendships an individual can
maintain.
• The number of nodes dynamically
changes based on birth and death
rate statistics.
Now, let’s look at our generation
algorithm.
Generation Algorithm
Acquaintance networks evolve as new
acquaintances form, old friendships
dissolve, and people join and leave
networks. New rules should consider
how individuals connect or disconnect with others in Chinese society.
Figure 1 shows a simulated flowchart
of our proposed model.
Our model operates as follows. Step
1 covers parameter initialization. According to statistical proportion, essential data is generated to initialize
the five basic attributes of each node.
This step assigns an initial fitness
value for each node and sets appropriate heredity and variation linking
proportions.
During Step 2, the network construction stage, an original network
is formulated with an initial number of N nodes and undirected edges
between pairs of nodes according to
network parameters.
7
NETWORK EVOLUTION MODELS
Start
Parameter initialization
Birth
Network construction
Size of nodes
Death
Evolution rules
N
Heredity linking
Size of connections
Variation linking
Stationary?
Similarity-based
disconnection
Y
End
Figure 1. Acquaintance network model flowchart. Step 1 is parameter initialization,
Step 2 is network construction, Step 3 is network evolution, and in Step 4 the
evolution is complete.
Step 3 handles network evolution.
During each time step, the size of
nodes and the scale of connections
both undergo variable change. The
dynamics of the model consist of the
following processes taking place at
each time step:
• Birth and death. According to each
year’s birth rate, new nodes arrive
and their attributes are initialized.
Old vertices are removed from the
acquaintance network at the year’s
death rate according to census data.
• Heredity and variation linking. Heredity linking and variation linking
are two dominant behaviors during
evolution.
• Similarity-based
disconnection.
Disconnection based on similarity denotes the social reality that
relationships are hard to maintain
between individuals with great
differences. Because the contacts
an individual can manipulate are
finite, if new acquaintances form
continually, an individual with
excessive degrees of connections
will break connections with some
8
acquaintances selectively. Disconnection based on minimum similarity is designed here to balance
the individual relation. It means
one randomly chosen node i will
remove the associated edge with
neighbor node j according to the
disconnection probability ( pijd ),
which is inversely proportional to
similarity as
pijd = 1 −
Sij
∑ Sil
,
l ∈ Li
where Li denotes the node collection of node i’s neighbors.
In Step 4, the evolution is completed. The simulation is over when
the simulation time comes to an end
or the network topological features
all achieves stationary states. If not,
the model jumps back to Step 3 and
continues the evolution process.
Heredity Linking
In the Chinese Guanxi-centered cultural environment, acquaintancewww.computer.org/intelligent
forming mainly derives from heredity
linking, which means a preference in
choice for neighbors of friends (here,
friends mean relatives or family).
According to the scale-free network
model, a node with a bigger degree
has a higher probability of forming
connections. However, this isn’t completely accordant with the reality of
friendship formation. When choosing
partners and establishing new relations, the individual not only considers
the quantity of another individual’s relations (degree k), he or she also values
the ability of the person to adapt to the
environment (fitness). If a person has
strong fitness, although his group of
friends is small, many individuals will
choose to become acquaintances with
him. Consequently, the linking probability phl
j that a randomly chosen node
i will be connected to node j depends
on the fitness (Fj) and the degree (kj) of
node j, so that
p hl
j =
Fj × kj
∑ ( Fm × km ) ,
m∈Mi
where Mi denotes the neighbor collection of node i’s neighbors.
The dynamics of the heredity process is defined as follows:
1. Randomly choose a node i from
the acquaintance network.
2. If the degree of node i reaches the
maximum value, reselect a random node. Randomly pick node
j from the neighbor collection of
node i’s neighbors (Mi).
3. If a random float number generated by the (0, 1) uniform distribution is lower than probability
p hl
j , insert an edge between nodes
i and j. If the heredity linking
number has reached the proportion number, heredity linking is
completed; otherwise, execute
from the beginning repeatedly.
IEEE INTELLIGENT SYSTEMS
Table 1. Statistical data from the fifth population census of China.
Gender (%)
Male
51.63
Age (%)
Female
Infants
Child
Juvenile
48.37
3.17
5.08
14.67
Proportion of education among the juvenile (%)
Illiteracy
2.68
Youth
Middle-aged
Elderly
37.61
29.76
9.71
Proportion of education among the youth (%)
Primary
Intermediate
Senior
Illiteracy
75.79
21.53
0
2.04
Proportion of education among the middle-aged (%)
Primary
Intermediate
Senior
21.63
70.35
5.98
Proportion of education among the elderly (%)
Illiteracy
Primary
Intermediate
Senior
Illiteracy
Primary
Intermediate
Senior
8.88
38.26
49
3.86
47.55
36.82
13.58
2.05
The heredity linking number is the
result of the size of nodes and the heredity proportion.
Variation Linking
Variation linking models the tendency of individuals to associate with
others based on occupational relations; acquaintance relation formation occurs on the basis of individual
social attributes. Variation means
choosing connected individuals based
on similarities adhering to preferential attachment. Linking the probability between nodes i and j ( pijvl ) is
calculated as
pijvl =
Sij
∑ Siq
,
q ∈Qi
where Qi denotes the collection of
those outside of node i’s neighbors.
The dynamics of the variation process is defined as follows:
1. Randomly choose a node i from
the acquaintance network.
2. If the degree of node i reaches the
maximum value, reselect a random node. Randomly pick node j
from the collection of those outside of node i’s neighbors (Qi).
3. If a random float number generated by the (0, 1) uniform distribution is lower than probability pijvl ,
insert an edge between node i and
j. If variation linking number has
reached the proportion number,
variation linking is completed;
SEPTEMBER/OCTOBER 2014
otherwise, execute from the beginning repeatedly.
The variation linking number is
jointly determined by the size of
nodes and variation proportion.
distribution as each node’s initial fitness. In this way, the probability that
RF exceeds 1 is larger, about 60 percent, indicating that individual fitness, compared to decrease, increases
with a higher probability. If it is above
1, Fi∗ will be set to 1.
Fitness Update Law
During the network evolution process,
the fitness of an individual dynamically changes as he or she establishes
new relations or loses contact with
others. The fitness update law is based
on the Matthew effect, which states
that an individual with strong fitness
will obtain stronger fitness and one
with weak fitness will obtain weaker
fitness. Thus, the updated fitness of
node i (Fi∗) is computed by
Fi∗ = λ × Fi + (1 − λ ) × RF × Fi ,
where l is a correction factor. To
avoid excessive numerical value correction, let l = 0.8, where RF is a
modified index. When individual fitness F is lower than the mean value
0.5, RF is a random number generated between [0, 1] according to the
(0.9995, 0.000592) normal distribution as each node’s initial fitness. In
this way, the probability that RF is
lower than 1 is larger, about 60 percent, indicating that individual fitness, compared to increase, decreases
with a higher probability. On the contrary, when individual fitness is larger
than the mean value 0.5, the value of
RF is generated between [0, 1] according to the (1.000 5, 0.000592) normal
www.computer.org/intelligent
Numerical Results
Using the fifth population census data
for China, this article uses the statistical data of gender proportion, age
proportion, population proportion in
different geographical positions, and
education-level proportion, respectively, in juvenile, youth, middle age,
and old age. We obtain the economic
condition in different regions as well.
Table 1 shows gender, age, and education proportions.
The simulation environment is designed as follows:
• Essential data of 5,000 nodes’ attributes is generated according to
the statistical proportion of the
fifth national census.
• Initial network is a random network with 5,000 nodes and connections per node set as four.
• The platform for essential data
generation is developed in C#. The
simulation environment is Anylogic
6.0, and the database is SQLServer
2008.
• The acquaintance network evolves
with a month time step.
Now, let’s look at how various parameters influence acquaintance networks.
9
NETWORK EVOLUTION MODELS
25
5.5
Weak effect
Medium effect
Strong effect
20
L
5.00
155
4.55
100
4.00
0
2
4
6
8
5
10
0
2
Time step (x 4 years)
4
6
8
10
Time step (x 4 years)
(a)
(b)
10–1
0.2
0.15
P(k)
10–22
C
0.1
10–33
0.05
0
0
(c)
2
4
6
8
Time step (x 4 years)
10
10–44
100
(d)
101
102
103
k
Figure 2. Comparison among the topological features for a Chinese traditional acquaintance network with a weak, medium,
and strong effect of Guanxi. (a) Average path length with time. (b) Average degree with time. (c) Clustering coefficient with
time. (d) Degree distribution.
Parameter Analyses: Effects
of Heredity Proportion
To determine the effects of heredity and variation on acquaintance
networks, we first define weak, medium, and strong effects of Guanxi
with parameters initialized at different levels of heredity proportion—10
percent, 20 percent, and 30 percent,
respectively—with a fixed variation
proportion of 5 percent, and then
run a series of simulations. Figure 2
shows that each of the four properties
10
eventually converges to an asymptotic stable value with the same trend.
Simulation results show a low degree
of separation and a high degree of
clustering, characteristic of the smallworld properties of social networks.
Under the weak effect of Guanxi,
topological features of the acquaintance networks change slowly, but
the average degree can rise to a stable
value rapidly with a strong effect of
Guanxi. Because of the inheritance of
relations in Chinese society, a person
www.computer.org/intelligent
can make acquaintances quickly.
Consequently, the parameters of a
strong effect of Guanxi are selected
as the best values.
Model Validation and Discussion
To validate our acquaintance network evolution model, we contrast
our simulation with the simulation
results of Davidsen’s model 5 for N =
5,000 and p = 0.0025 and Huang’s
model6 for N = 5,000, p = 0.0025, b =
0.0001, f 0 = beta 14(0.5), q = 0.1,
IEEE INTELLIGENT SYSTEMS
Davidsen’s
Huang’s
CTAN
L
5.0
4.5
4.0
3.5
0
2
4
6
Time step
8
10
(a)
30
0.6
25
0.5
20
0.4
15
0.3
C
5.5
10
0.2
5
0.1
0
0
0
2
4
6
Time step
8
0
10
2
8
4
6
Time step
10
(c)
(b)
Figure 3. Comparison of topological features for Chinese traditional acquaintance network (CTAN), Davidsen’s network, and
Huang’s network. One time step in CTAN stands for four years; in Davidsen’s network and Huang’s network, it stands for
10,000 steps. (a) Average path length with time. (b) Average degree with time. (c) Clustering coefficient with time.
SEPTEMBER/OCTOBER 2014
100
2
Population proportion
38.06%
8.84%
52.02%
10–1
P(k)
q = 0.4, r = 1.0, b = 0.0001, which
is the best match for actual social activity scenarios according to the two
literatures.
Figure 3 presents the contrasting
result of average degree, clustering
coefficient, and average path length
with respect to time. From the result, it can be seen that the variation
trend of topological features of our
network is similar to the features of
Davidsen’s network. They both share
fluctuations, but there are differences
among the stable values of the three
metrics. The average degree of our
network can be stabilized in a shorter
time than Davidsen’s network. This
can be explained by the phenomenon
in Chinese rural society wherein close
relatives can be inherited from families quickly as stable acquaintance relationships. Comparatively speaking,
developed Western countries don’t
depend so heavily on kinship to facilitate interpersonal communication.
However, average path length in our
acquaintance network is longer than
in Davidsen’s, and the clustering coefficient in our acquaintance network
is lower than both Davidsen’s network and Huang’s network. We postulate that the corresponding social
phenomenon for this data is the normal existence of multigenerational
settled groups of individuals in the
Davidsen’s
Huang’s
CTAN
Power-law distribution
with an exponential cutoff
Exponential distribution
10–2
3
1
10–3
Population proportion
16.24%
0.38%
11.82%
Population proportion
45.7%
90.78%
36.16%
10–4
100
101
k
102
Figure 4. Comparison of the degree distribution for a Chinese traditional
acquaintance network (CTAN), Davidsen’s network, and Huang’s network. The
population proportions of the three networks in each segmentation are presented.
vast Chinese rural areas. Only a few
individuals are in contact with communities outside the kinship area.
Isolation characterizes the typical
relationship between these different
communities. Due to the third rule of
friendship updates in Huang’s model,
a large number of relations are disconnected, leading to a decrease in
www.computer.org/intelligent
the average degree and higher average
path length compared to the other
two networks.
Figure 4 shows the degree distribution of acquaintance networks
using the three models. According
to the degree distribution characteristics, we divided the population
proportions of the three networks
11
NETWORK EVOLUTION MODELS
into three segmentations for discussion. In Segmentation I, with a small
number of degrees, the population
proportion of our network (36.16
percent) is lower than the other two
networks (45.7 percent and 90.78
percent), indicating that individuals with few relations are less prevalent than in the other two networks.
In a group with few social relations,
there’s only a small minority. In Segmentation II, with a medium number
of degrees, our network’s degree distribution shows a slow decline, while
those of the other two networks fall
rapidly. The population proportion
of our network (52.02 percent) is
higher in the middle than the other
two networks (38.06 percent and
8.84 percent). The results illustrate
that most individuals maintain some
medium number of connections
through the inheritance mechanism.
In Segmentation III, with a sufficiently high number of degrees, the
three networks’ degree distribution
shows an emergent tendency of rapid
decrease, indicating that people who
own large numbers of social relations represent a small portion of the
total. On the whole, degree distribution in Davidsen’s network exhibits
a power-law regime for small p, and
Huang’s model produces a distribution feature that mixes power-law
and exponential distribution types.
In Segmentations I and II, our network displays a power-law form
with an exponential cutoff: P(k) ∼
e −bk(k + c) −g , the fitting parameters
of which are b = 0.0371, c = 0.974,
and g = 0.1064. In Segmentation III,
it follows an exponential distribution: P(k) ∼ le −lk, the parameter of
which is l = 0.0487.
Through comparative analysis, the
numerical results of our model provide valid explanations for some
widely accepted sociological conclusions pertaining to Chinese rural
12
society structure. Individuals with
relatively few relations in the Chinese hierarchical context are less
prominent than they are in Western societies, corresponding to Segmentation I. The implications of our
results support the view that the Chinese family is a tiny nation, shaping
its community by self-organization,
a familial rather than social integration noticed by American scholar
John King Fairbank.15 People with
medium degrees of relations in Segmentation II constitute the largest
proportion, an observation well explained in Fei’s classic conclusions.
Fei13 pointed out that, in China,
distribution of peak values in the
middle segmentation.
However, the opposing feature
of a large number of individuals in
Segmentation I in Western societies is due to group characteristics.
The Western acquaintance relationship is more equal and concise, and
can be conceived of as a metaphor,
the fasces, or sticks of wood bounded
together in parallel to each other. Individuals are independent, and acquaintance relationships don’t rely on
blood kinship. Taken as a whole, the
basic features in Chinese and Western society are totally different, and
the analysis of our network matches
well with the conclusions of sociological research.
The formation of
traditional acquaintance
relationships is greatly
affected by the special
Chinese kinship culture in
a Guanxi-centered society.
each person is part of a kinship network based on the axis of relatives.
Numerous kinship networks overlap
to form Chinese traditional acquaintance relationships. Compared with
Western countries, the Chinese traditional social structure is typically
an interpersonal interaction relationship network linked by blood, relative, and geographical relationships.
Kinship culture marks this acquaintance society more strongly than in
Western countries. As a result, individuals with medium relations constitute the largest proportion. The
characteristics of the Chinese acquaintance society in turn verify the
www.computer.org/intelligent
I
n this article, we introduced a
model of a Chinese traditional acquaintance network. In contrast to
previous acquaintance network models, we emphasize individual heterogeneity and social culture, and
incorporate three distinct mechanisms that result in acquaintance relationship formation and separation,
respectively: heredity linking, variation linking, and similarity-based
disconnection. Compared with the
acquaintance networks in Western
countries, our network shows irregular characteristics. The degree
distribution of Chinese traditional
acquaintance networks is manifested
as a piecewise approximation that
combines a power-law form with
an exponential cutoff and distribution. Numerical results show that
individuals with few or many relations in a Chinese hierarchical system are neither representative nor
especially prominent, and individuals whose degree is around the average value instead constitute the
largest proportion of the whole.
These results further indicate that the
IEEE INTELLIGENT SYSTEMS
THE AUTHORS
Xi Chen is an associate professor in the School of Automation at the Huazhong University of Science and Technology. His research interests include modeling and simulation,
agent and multiagent systems, emergency management, complex networks, artificial intelligence, and computational social science. Chen has a PhD in systems engineering from
the Huazhong University of Science and Technology. He’s a member of IEEE, a member
of the Artificial Intelligence Society of China, and a senior member of the Chinese Institute of Electronics. Contact him at chenxi@mail.hust.edu.cn.
Lan Zhang is a master’s student in the School of Automation at the Huazhong University of Science and Technology. Her research interests include social network modeling
and analysis, and multiagent systems. Zhang has a BS in systems engineering from the
Huazhong University of Science and Technology. Contact her at zhanglan1107@gmail.
com.
Wei Li is an associate professor in the School of Automation at the Huazhong University
of Science and Technology. Her research interests include modeling and simulation theory and application, complex systems science, intelligent control, and brain networks. Li
has a PhD in control science and engineering from the Huazhong University of Science
and Technology. She’s a member of IEEE and the Artificial Intelligence Society of China.
Contact him at liwei0828@mail.hust.edu.cn.
formation of traditional acquaintance
relationships is greatly affected by the
special Chinese kinship culture in a
Guanxi-centered society. Our findings are supported by sociological
statistical conclusions and offer a rational explanation for the nature of
Chinese kinship networks.
Still, there are some issues requiring
further study to achieve a better understanding of the structure of complex social networks. For example,
the individual attributes studied are
incomplete, and the cultural elements
considered are only partially representative of a real, complex society.
How different attributes affect network topology remains an interesting
topic for extensive study in the near
future.
Our work provides an adequate
framework for further research on
dynamic and complex human behaviors, such as epidemics spreading or rumors propagating. The
effect of network topology on information diffusion can be further explored in specified social networks.
Ultimately, our work contributes to
a greater emphasis on cultural diversity as a basic consideration for modeling more accurate acquaintance
networks.
SEPTEMBER/OCTOBER 2014
Acknowledgments
This work was supported by the National
Natural Science Foundation of China
(grant NSFC 70903026), the Fundamental
Research Funds for the Central Universities (HUST:2013TS125), and the Key Laboratory of Ministry of Education for Image
Processing and Intelligent Control, China.
We thank Xiaolei Yang for proving essential
data and Qin Tu for developing the simulation platform. We’re grateful to those people
who provided useful reference articles and
contributed their valuable suggestions.
References
1. S. Staab et al., “Social Networks Applied,” IEEE Intelligent Systems, vol.
20, no. 1, 2005, pp. 80–93.
2. B. Bringmann et al., “Learning and
Predicting the Evolution of Social Networks,” IEEE Intelligent Systems, vol.
25, no. 4, 2010, pp. 26–35.
3. G. Bianconi and A. Barabási, “BoseEinstein Condensation in Complex
Networks,” Physical Rev. Letters, vol.
86, 2001, pp. 5632–5635.
4. E.M. Jin, M. Girvan, and M.E.J. Newman, “Structure of Growing Social
Networks,” Physical Rev. E, vol.
64, no. 046132, 2001; http://dx.doi.
org/10.1103/PhysRevE.64.046132.
5. J. Davidsen, H. Ebel, and S. Bornholdt,
“Emergence of a Small World from
Local Interactions: Modeling Acquaintance Networks,” Physical Rev. Letters,
www.computer.org/intelligent
vol. 88, no. 12, 2002; http://dx.doi.
org/10.1103/PhysRevLett.88.128701.
6. C.Y. Huang and Y.S. Tsai, “Effects
of Friend-Making Resources Costs
and Remembering on Acquaintance
Networks,” Physica A, vol. 389, no. 3,
2010, pp. 604–622.
7. M. Boguñá et al., “Models of Social
Networks Based on Social Distance
Attachment,” Physical Rev. E, vol. 70,
no. 056122, 2004, doi:10.1103/
PhysRevE.70.056122.
8. D.J. Watts and S.H. Strogatz, “Collective Dynamics of ‘Small World’
Networks,” Nature, vol. 393, 1998, pp.
440–442; doi:10.1038/30918.
9. R. Albert and A.L. Barabasi, “Emergence of Scaling in Random Networks,”
Science, vol. 286, no. 5439, 1999, pp.
509–512.
10. M.S. Granovetter, “The Strength of
Weak Ties,” Am. J. Sociology, vol. 78,
no. 6, 1973, pp. 1360–1380.
11. S.H. Park and Y. Luo, “Guanxi and
Organizational Dynamics: Organizational Networking in Chinese Firms,”
Strategy Management J., vol. 22, 2001,
pp. 455–477.
12. X.P. Chen and C. Chen, “On the Intricacies of the Chinese Guanxi: A Process
Model of Guanxi Development,” Asia
Pacific J. Management, vol. 21, 2004,
pp. 305–324.
13. X.T. Fei, From the Soil: The Foundations of Chinese Society, Peking Univ.
Press, 1998 (in Chinese).
14. X. Zhai, “Trait of Chinese Interpersonal Relationship,” Sociological Research,
vol. 4, 1993, pp. 74–83 (in Chinese).
15. J.K. Fairbank, The United States and
China, Harvard Univ. Press, 1948.
Selected CS articles and columns
are also available for free at
http://ComputingNow.computer.org.
13