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
Chinese traditional
acquaintance
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.
Indeed, little attention is paid to offline so-cial relationships. The technique of link prediction from a constructivist view has helped users make implicit connections through online websites with those of simi-lar interests.2 With respect to acquaintance relationships, the general method of how to represent the processes and results of rela-tion formarela-tion in real life remain unclear. Such networks are conceived by researchers as a crucial way for people to exchange in-formation 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 mod-els that correspond well to features of social networks in real life have been pro-posed.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 forma-tion transacforma-tion costs and retenforma-tion costs were considered for improvement in
Chung-Yuan Huang and Yu-Shiuan Tsai’s model.6
Marián Boguñá and his colleagues7
stud-ied 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 re-wiring mechanism has been found to lie in small-world networks,8 and preferential at-tachment 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 rela-tions, Mark S. Granovetter proposed two
S
ocial networks have attracted a great deal of interest from
research-ers in different scientific fields. Existing applications of social networks
mainly investigate topological features and evolution mechanisms from data—
N E T W O R K E V O L U T I O N M O D E L S
definitions: strong ties and weak
ties.10 This theory, however,
inad-equately applies to the Chinese case due to the specific forms of Chi-nese acquaintance communication. Guanxi is proposed as an essential element of everyday social life that infiltrates every aspect of Chinese so-ciety. 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 con-nections to secure favors in personal and organizational relations. Xiao-tong 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. Ac-cording to Fei, Chinese traditional acquaintance relationships are built with close family members at the core and distant relatives, classmates, and friends arranged on the periph-ery according to the distance of the relationship and the degree of trust.
Family principle,14 where the
fam-ily is the basis of society, is perhaps more true of China than of any other highly developed nation. Acquain-tance communication depends on the natural “blood” and geographic re-lationships that are characteristic of the Chinese special kinship culture. Generations of deeply rooted indi-viduals are the normal state of soci-ety. Isolation, however, is also present between different communities as in-dividuals survive on their own in a vast rural area. Consequently, the ac-quaintance communication under a Chinese cultural environment is dif-ferent from other types of societies.
Previously developed acquaintance network models have shown the ex-istence of small-world properties and scale-free features, but they as-sume that nodes are the same and fail to take different social cultures into account. In this study, we incorporate
three new mechanisms—heredity linking, variation linking, and simi-larity-based disconnection—to form an evolution model of the Chinese acquaintance relationship network. Combined with actual statistical birth and death rate data, our numer-ical results not only show small-world characteristics but also imply the na-tive characteristics of a Guanxi- centered society that are absent in other models of social networks.
Topological Features of Acquaintance Networks
To put forward our model of ac-quaintance 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 in-dividuals in social networks were as-sumed to be identical. But obviously, different social individuals manifest different social attributes and pref-erences to acquaint themselves with others. In our model, five basic at-tributes forming an attribute set represent the heterogeneity among in-dividuals. Specifically, attribute sets of individual (node) i contain the fol-lowing attributes:
• agei is a nonnegative integer
repre-senting node i’s age;
• genderi is specified as male or
fe-male according to node i’s gender;
• edui is an assignment for
educa-tion level of node i—it’s quantified as a float number between 0 and 1, where 0 stands for the lowest edu-cation 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
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 pro-posed to calculate the similarity between users in collaborative rec-ommender systems. With respect to our acquaintance networks, similar-ity is defined as the attraction degree among people. Acquaintance com-munication shows that you’re more likely to establish or maintain a so-cial 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 differ-ent types of value, Sij is categorized into identical similarity (Sij1), degree
similarity (Sij2), and reverse similar-ity (Sij3).
For identical similarity, Sij1 is
de-fined for attributes with only two val-ues. Here, only gender is included. Sij1
is quantified as
= ≠
0 , gender gender 1 , gender gender .
in terms of the attribute with a float number. Here, age similarity (Sijage), education similarity (Sijedu), and
econ-omy similarity (Sijeco) are included.
Sijage is measured as
eco are calculated in
the same way. Then, Sij2 is summed as
= ⋅
proportional to distance between two nodes, based on the Hamming dis-tance. Sij3 is computed as
= − − + −
S
d
1 (gpx gpx ) (gpy gpy ) ,
ij
i j i j
3
2 2
max
where dmax is the maximum distance
among all nodes. By combining Sij1, S
ij2, and Sij3, Sij is
computed as
= ⋅
Sij [w w w1, 2, 3] [S S S1ij, ij2, ij3] ,T
where w1, w2, and w3 are the weights of each kind of similarity specified by experts. For convenience of calcula-tion, the values of similarity are nor-malized 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 follow-ing the ideas of heredity and variation. In Chinese traditional rural soci-ety, social relationship structure is dominated by extreme particularism. Blood/geographical relations are ba-sic social relations attached to tradi-tional 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 probabil-ity than strangers—that is, most ac-quaintance network relationships are naturally inherited from family and irrelevant to an individual’s attributes. This kinship, resulting from marriage and procreation, is the most perva-sive relationship in Chinese society. Each person has a kinship network,
more likely to make friends through acquaintances. We assume that the central mechanism of the dynamics of acquaintance networks is that peo-ple are introduced to each other by a common acquaintance.
People generally tend to associ-ate with family members. Only when the family group can’t meet the de-mand will they consider associating and forming relations with strang-ers. In some cases, people become acquainted based on occupational relations or other common charac-teristics. Variation is developed into our acquaintance model to describe such tendencies. Acquaintanceship is generally influenced by individual so-cial attributes, which means that you have higher linking probability to an-other person due to high similarity, adhering to preferential attachment.
Fitness
A fitness parameter is defined to mea-sure different individual abilities for environmental adaptation, which af-fects the process of making connec-tions with others. Fi is assigned to
node i to denote the fitness of node i. It’s quantified as a float number be-tween 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 rel-atively 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
• According to Chinese law, an
indi-vidual over 16 years old is sexually mature and has reached the age of consent. Taking individual cog-nition into consideration, it’s as-sumed that individuals over 16 years old have the ability of hered-ity and variation.
• Because individual resources and
friend-making costs are finite, there’s an upper limit on the num-ber 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 discon-nect 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. Ac-cording to statistical proportion, es-sential data is generated to initialize the five basic attributes of each node. This step assigns an initial fitness value for each node and sets appro-priate heredity and variation linking proportions.
During Step 2, the network con-struction stage, an original network is formulated with an initial
num-ber of N nodes and undirected edges
N E T W O R K E V O L U T I O N M O D E L S
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.
He-redity linking and variation linking are two dominant behaviors during evolution.
• Similarity-based disconnection.
Disconnection based on similar-ity denotes the social realsimilar-ity 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
acquaintances selectively. Discon-nection based on minimum simi-larity 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
tion of node i’s neighbors.
In Step 4, the evolution is com-pleted. 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 cul-tural environment,
acquaintance-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 com-pletely accordant with the reality of friendship formation. When choosing partners and establishing new rela-tions, the individual not only considers the quantity of another individual’s re-lations (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 proba-bility phlj that a randomly chosen node
where Mi denotes the neighbor
collec-tion of node i’s neighbors.
The dynamics of the heredity pro-cess 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 ran-dom node. Ranran-domly pick node
j from the neighbor collection of
node i’s neighbors (Mi).
3. If a random float number gener-ated by the (0, 1) uniform distri-bution is lower than probability
pjhl, insert an edge between nodes
i and j. If the heredity linking number has reached the propor-tion number, heredity linking is completed; otherwise, execute from the beginning repeatedly.
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.
Start
Parameter initialization
Size of nodes
Size of connections
The heredity linking number is the result of the size of nodes and the he-redity proportion.
Variation Linking
Variation linking models the ten-dency of individuals to associate with others based on occupational rela-tions; acquaintance relation forma-tion occurs on the basis of individual social attributes. Variation means choosing connected individuals based on similarities adhering to preferen-tial attachment. Linking the prob-ability between nodes i and j (pijvl) is
calculated as
∑
=∈
p S
S ,
ij
vl ij
iq q Qi
where Qi denotes the collection of
those outside of node i’s neighbors. The dynamics of the variation pro-cess 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
ran-dom node. Ranran-domly pick node j
from the collection of those out-side of node i’s neighbors (Qi).
3. If a random float number gener-ated by the (0, 1) uniform distribu-tion 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;
otherwise, execute from the be-ginning repeatedly.
The variation linking number is jointly determined by the size of nodes and variation proportion.
Fitness Update Law
During the network evolution process, the fitness of an individual dynami-cally 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
λ λ
= × + − × ×
∗
Fi Fi (1 ) RF Fi,
where l is a correction factor. To
avoid excessive numerical value cor-rection, let l = 0.8, where RF is a modified index. When individual
fit-ness F is lower than the mean value
0.5, RF is a random number
gener-ated between [0, 1] according to the (0.9995, 0.000592) normal distribu-tion as each node’s initial fitness. In this way, the probability that RF is lower than 1 is larger, about 60 per-cent, indicating that individual fit-ness, compared to increase, decreases with a higher probability. On the con-trary, when individual fitness is larger than the mean value 0.5, the value of RF is generated between [0, 1] accord-ing to the (1.000 5, 0.000592) normal
distribution as each node’s initial fit-ness. In this way, the probability that RF exceeds 1 is larger, about 60 per-cent, indicating that individual fit-ness, compared to decrease, increases with a higher probability. If it is above 1, Fi∗ will be set to 1.
Numerical Results
Using the fifth population census data for China, this article uses the statis-tical data of gender proportion, age proportion, population proportion in different geographical positions, and education-level proportion, respec-tively, in juvenile, youth, middle age, and old age. We obtain the economic condition in different regions as well. Table 1 shows gender, age, and edu-cation proportions.
The simulation environment is de-signed as follows:
• Essential data of 5,000 nodes’
at-tributes is generated according to the statistical proportion of the fifth national census.
• Initial network is a random
net-work with 5,000 nodes and con-nections 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 param-eters influence acquaintance networks.
Proportion of education among the juvenile (%) Proportion of education among the youth (%)
Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior
2.68 75.79 21.53 0 2.04 21.63 70.35 5.98
Proportion of education among the middle-aged (%) Proportion of education among the elderly (%)
Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior
N E T W O R K E V O L U T I O N M O D E L S
Parameter Analyses: Effects of Heredity Proportion
To determine the effects of hered-ity and variation on acquaintance networks, we first define weak, me-dium, and strong effects of Guanxi with parameters initialized at differ-ent 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
eventually converges to an asymp-totic stable value with the same trend. Simulation results show a low degree of separation and a high degree of clustering, characteristic of the small-world properties of social networks. Under the weak effect of Guanxi, topological features of the acquain-tance 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
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 net-work evolution model, we contrast our simulation with the simulation results of Davidsen’s model5 for N=
5,000 and p = 0.0025 and Huang’s
model6 for N= 5,000, p= 0.0025, b= 0.0001, f0 = beta 14(0.5), q = 0.1, 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.
5.5 25
10–1
10–2
10–3
10–4
100 101 102
k
103
20
15
10
5 5.0
4.5
L
C
<k>
P(k)
4.0
0.2
0.15
0.1
0.05
0
0 2 4 6 8
Time step (x 4 years)
10
0 2 4 6 8
Time step (x 4 years)
10
0 2 4 6 8
Time step (x 4 years)
10 5
0
2
3
4
Weak effect
Medium effect
Strong effect
(a) (b)
(c) (d)
0
5
0
Medium effect
q = 0.4, r = 1.0, b = 0.0001, which is the best match for actual social ac-tivity 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 re-sult, 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 fami-lies quickly as stable acquaintance re-lationships. Comparatively speaking, developed Western countries don’t depend so heavily on kinship to fa-cilitate interpersonal communication. However, average path length in our acquaintance network is longer than in Davidsen’s, and the clustering co-efficient in our acquaintance network is lower than both Davidsen’s net-work and Huang’s netnet-work. We pos-tulate that the corresponding social phenomenon for this data is the nor-mal existence of multigenerational settled groups of individuals in the
vast Chinese rural areas. Only a few individuals are in contact with com-munities 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 dis-connected, leading to a decrease in
the average degree and higher average path length compared to the other two networks.
Figure 4 shows the degree distri-bution of acquaintance networks using the three models. According to the degree distribution charac-teristics, we divided the population proportions of the three networks
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.
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.
(c)
0.2
0.1
0
0 2 4 6
Time step
8 10
10
5
0
0 2 4 6 8 10
(b)
Time step
<k>
4.0
3.5
(a)
0 2 4 6
Time step
8 10
100
10–1
1
2
3
Population proportion 45.7% 90.78% 36.16%
Population proportion 38.06% 8.84% 52.02%
Population proportion 16.24% 0.38% 11.82% Davidsen’s Huang’s CTAN
Power-law distribution with an exponential cutoff Exponential distribution
10–2
10–3
10–4
100
101 102
k
P
(
k
N E T W O R K E V O L U T I O N M O D E L S
into three segmentations for discus-sion. 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 individu-als with few relations are less preva-lent than in the other two networks. In a group with few social relations, there’s only a small minority. In Seg-mentation II, with a medium number of degrees, our network’s degree dis-tribution 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 suffi -ciently 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 rela-tions represent a small portion of the total. On the whole, degree distribu-tion in Davidsen’s network exhibits
a power-law regime for small p, and
Huang’s model produces a distribu-tion feature that mixes power-law and exponential distribution types. In Segmentations I and II, our net-work displays a power-law form with an exponential cutoff: P(k) ∼ e−bk(k + c)−g, the fi tting parameters
of which are b = 0.0371, c = 0.974,
and g= 0.1064. In Segmentation III,
it follows an exponential distribu-tion: P(k) ∼ le−lk, the parameter of
which is l= 0.0487.
Through comparative analysis, the numerical results of our model pro-vide valid explanations for some widely accepted sociological con-clusions pertaining to Chinese rural
society structure. Individuals with relatively few relations in the Chi-nese hierarchical context are less prominent than they are in West-ern societies, corresponding to Seg-mentation I. The implications of our results support the view that the Chi-nese family is a tiny nation, shaping its community by self-organization, a familial rather than social integra-tion noticed by American scholar
John King Fairbank.15 People with
medium degrees of relations in Seg-mentation II constitute the largest proportion, an observation well ex-plained in Fei’s classic conclusions.
Fei13 pointed out that, in China,
each person is part of a kinship net-work based on the axis of relatives. Numerous kinship networks overlap to form Chinese traditional acquain-tance relationships. Compared with Western countries, the Chinese tra-ditional social structure is typically an interpersonal interaction relation-ship network linked by blood, rela-tive, and geographical relationships. Kinship culture marks this acquain-tance society more strongly than in Western countries. As a result, indi-viduals with medium relations con-stitute the largest proportion. The characteristics of the Chinese ac-quaintance society in turn verify the
distribution of peak values in the middle segmentation.
However, the opposing feature of a large number of individuals in Segmentation I in Western societ-ies is due to group characteristics. The Western acquaintance relation-ship 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. In-dividuals are independent, and ac-quaintance relationships don’t rely on blood kinship. Taken as a whole, the basic features in Chinese and West-ern society are totally different, and the analysis of our network matches well with the conclusions of sociolog-ical research.
I
n this article, we introduced amodel of a Chinese traditional ac-quaintance network. In contrast to previous acquaintance network mod-els, we emphasize individual het-erogeneity and social culture, and incorporate three distinct mecha-nisms that result in acquaintance re-lationship formation and separation, respectively: heredity linking, varia-tion linking, and similarity-based disconnection. Compared with the acquaintance networks in Western countries, our network shows ir-regular 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 distribu-tion. Numerical results show that individuals with few or many rela-tions in a Chinese hierarchical sys-tem are neither representative nor especially prominent, and individu-als whose degree is around the av-erage value instead constitute the largest proportion of the whole. These results further indicate that the
The formation of
formation of traditional acquaintance relationships is greatly affected by the special Chinese kinship culture in a Guanxi-centered society. Our find-ings are supported by sociological statistical conclusions and offer a ra-tional explanation for the nature of Chinese kinship networks.
Still, there are some issues requiring further study to achieve a better un-derstanding of the structure of com-plex social networks. For example, the individual attributes studied are incomplete, and the cultural elements considered are only partially repre-sentative of a real, complex society. How different attributes affect net-work 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 be-haviors, such as epidemics spread-ing or rumors propagatspread-ing. The effect of network topology on infor-mation diffusion can be further ex-plored in specified social networks. Ultimately, our work contributes to a greater emphasis on cultural diver-sity as a basic consideration for mod-eling more accurate acquaintance networks.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (grant NSFC 70903026), the Fundamental Research Funds for the Central Universi-ties (HUST:2013TS125), and the Key Labo-ratory 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 simula-tion platform. We’re grateful to those people who provided useful reference articles and contributed their valuable suggestions.
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Selected CS articles and columns are also available for free at http://ComputingNow.computer.org.
telligence, 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 Insti-tute 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 Univer-sity 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.
