Bidirectional selection between two
classes in complex social networks
Bin Zhou
1,2
, Zhe He
1
, Luo-Luo Jiang
3
, Nian-Xin Wang
2
& Bing-Hong Wang
1,3
1
Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China,
2
School of Economics and
Management, Jiangsu University of Science and Technology, Zhenjiang, 212003, China,
3
College of Physics and Electronic
Information Engineering, Wenzhou University, Wenzhou, 325035, China.
The bidirectional selection between two classes widely emerges in various social lives, such as commercial
trading and mate choosing. Until now, the discussions on bidirectional selection in structured human
society are quite limited. We demonstrated theoretically that the rate of successfully matching is affected
greatly by individuals’ neighborhoods in social networks, regardless of the type of networks. Furthermore, it
is found that the high average degree of networks contributes to increasing rates of successful matches. The
matching performance in different types of networks has been quantitatively investigated, revealing that the
small-world networks reinforces the matching rate more than scale-free networks at given average degree. In
addition, our analysis is consistent with the modeling result, which provides the theoretical understanding
of underlying mechanisms of matching in complex networks.
U
nderstanding the pattern of human activities has been received growing attention due to it’s important
practical applications from traffic management to epidemic control
1–4
. Several mechanisms with indi-
vidual activities have been discovered based on statistics of huge amounts of data on human behaviors,
such as queueing theory and adaptive interest
5–7
. However, mechanisms behind human activities with interacting
individuals are far from well understood because of complex population structures which can be described by
complex networks
8–10
. Apart from the statistic characteristics of human dynamics in space and time interval,
abundant researches have focused on comprehending human activities in social networks such as making friends
where people in the same class with similar feature are more likely to be friends. There are also common
phenomena of seeking social partners belonging two classes in bipartite populations
11,12
, such as mate choosing
between men and women, commercial trading between buyers and sellers.
The seeking processes which may be the base of building many social relationships can be described by
matching model
13
. Individuals are generally divided into two classes according to their natural status. Then
they observe features of others belonging to the other class, and finally de cide whether select the individual as
a social partner. Although characters of individuals are too complex to be quantitatively described in
bidirectional selection syste ms, personal quality and economic status can be viewed as the main characters
of individuals
14,15
. Zhang and his collaborators solve the bipartite matching problem in the framework of
economic markets, finding that partial informat ion and bounded ratio-nality cont ribute to satisfied and
stable match es
16,17
. Besides characters of individuals, the mat ching processes is also affected by structure
of social networks
18–20
. Since social networks have emerged some common characteristics, such as small-
world phenomena, scale-free properties with power-law degree distributions
21,22
. Que stions naturally arise
how properties of social networks affect matching processes, and what kind of the property improves the
matching performance of networks. To answe r these questions, a bipartite network is reconstructed from the
original networks
23–25
, where only connected nodes satisfy ing successfully matching conditions and their
links ar e reserved. This allows us to investigate the bidirectional matching processes with mathematical
analysis and computer simulati on.
In this paper, we researched the matching problem of two classes in the framework of complex net-
works. The analytical solution for the rate of successfully matching rate is presented, which is consistent
with our simulation results of matching processes on social networks. It is observed that properties of
networks greatly i mpact matching performance of networks, and the small-world effect improve rate of
successfully matching more than scale-free properties. In addition, the small-world effect on matching
performance of networks was quantitatively investigated with different rewiring rate in the small world
network.
OPEN
SUBJECT AREAS:
NONLINEAR
PHENOMENA
COMPLEX NETWORKS
Received
20 June 2014
Accepted
2 December 2014
Published
19 December 2014
Correspondence and
requests for materials
should be addressed to
L.-L.J. (jiangluoluo@
gmail.com)
SCIENTIFIC REPORTS | 4 : 7577 | DOI: 10.1038/srep07577 1