J. Software Engineering & Applications, 2008, 1: 53-59
Published Online December 2008 in SciRes (www.SciRP.org/journal/jsea)
Copyright © 2008 SciRes JSEA
Motif-based Classification in Journal Citation Networks
Wenchen Wu
, Yanni Han
, Deyi Li
(State Key Lab of Software Development Environment, Beihang University, Beijing, 100083, China),
(Institute of Electronic
System Engineering, Beijing, 100039, China)
Email: wuws@nlsde.buaa.edu.cn, ziqinli@public2.bta.net.cn, libra_hyn@sina.com
Received November 16
, 2008; revised November 20
, 2008; accepted November 27
, 2008.
Journals and their citation relations are abstracted into journal citation networks, basing on CSTPC journal database
from year 2003 to 2006. The network shows some typical characteristics from complex networks. This paper presents
the idea of using motifs, subgraphs with higher occurrence in real network than in random ones, to discover two
different citation patterns in journal communities. And a further investigation is addressed on both motif granularity
and node centrality to figure out some reasons on the differences between two kinds of communities in journal citation
Motif, Classification, Journal Citation Networks
1. Introduction
As an effective method, complex networks have been
widely used to describe many complicated real world
systems. It can be regarded as the topology abstract of
many real complex systems, whose structure do not rely
on node position or edge form, but with two essential
attributes-small-world [1] and scale-free [2].
Though many networks present common global
characteristics, they could have entirely different local
structures. Recent researches indicate that network motifs,
interconnected patterns occurring in numbers that are
significantly higher than those in identical randomized
networks, may be the “simple building blocks” in
complex networks [3]. The concept and applications of
motifs are first appeared in biological field. They present
in biological systems as characteristic modules to carry
out some certain kind of functions. For example, the
same motifs, defined as feed-forward loops, have been
found in organisms from bacteria and yeast [4], to plants
and animals [5,6]. This kind of motifs plays an important
role of persistence detectors, or pulse generator and
response accelerators. These kinds of research results
always make some direct biology meanings [7]
with certain iterations, many small, highly connected
topologic motifs could combine in a hierarchical manner
into larger but less cohesive modules [8].
Ron Milo proposed two concepts in 2002, which are
shown below to find motifs in networks. And then they
gave the concept of “superfamilies” in 2004 and also the
significance profile (SP) method to compare the local
structure between different kinds of complex networks
[9]. The result shows that networks from different fields
can share similar characteristic of local structures.
Z-Score, valuing the statistic importance of each
network motifs
( )
P-Value means the probability of network motifs
appearing in a randomized network an equal or greater
number of times than in the real network.
Milo and his fellows also published the motif detection
software, named MFinder in the homepage of Uri Alon
lab. In MFinder, the subgraphs need to satisfy the default
settings to make themselves network motifs, in which
their Z-Score should bigger than 2, and P-Value should
less than 0.05. Figure 1 shows a motif detection in real
network and random network respectively by Ron Milo.
The reminder of this paper is organized as follows.
Section 2 outlines the construction and essential attributes
of journal citation networks. Section 3 presents the
degree analysis of the networks. Section 4 analyses the
motif structures and citation patterns in journal
communities, and Section 5 concludes the whole work
and discusses future research directions.
2. Construction Principles and Attribute
This article obtains the original data from a project led by
the Institute of Scientific and Technical Information of
China in 2004 [10]. The project formed both the citing
and cited matrixes of each journal, which is embodied in
China Scientific and Technical Papers and Citations
(CSTPC) database from year 2003 to 2006 respectively.
The journal citation networks are constructed according
to those matrixes.
54 Motif-based Classification in Journal Citation Networks
Copyright © 2008 SciRes JSEA
Figure 1. Motif detection in networks
In this paper, we define a journal citation network as
follows: each journal expresses as a node of network, if
one journal cites others, an edge is added beginning with
this journal and ending with the journal it cites.
Otherwise, if one journal is cited by other ones, then add
an edge beginning with the journal which cites it and
ending with this journal. After sorting one-year journals
this way, a directed journal citation network can finally
be formed.
This article presents many essential attributes in
journal citation networks of these four years. For instance,
network connectivity, network diameter, average path
length and also average clustering coefficient. Table 1
shows some fundamental statistic information. It can be
found that network scale grows steadily from the year
2003 to 2006, except a sharply edge decrease in the year
2005. According to a further investigation, this phenomenon
has something to do with a limited threshold in the
original datasets, which is set up to filtrate the noise data.
The average degree can explain average citation times
between journals. It shows that the citation is more
positive in 2006 than other years. Meanwhile, network
diameters are no bigger than six in the year 2003, 2004
and 2006, and these networks also have big average
clustering coefficient, which indicate typical small-world
characteristic commonly in complex networks.
3. Degree Analysis
Degree is a simple but important definition to describe
node attributes, which can reflect some network
characteristics intuitively. When it comes to directed
journal networks, a node’s outdegree is the number of
journals it cites, and its indegree is the number of journals
citing it. Figure 2 shows the indegree and outdegree
distributions of these four years. It is obvious that the
nodes whose indegree or outdegree are bigger than 10,
are in accordance with power-law distribution, which
means a typical scale-free characteristic. Most nodes of
small degrees have few cited or citing relations, but in
contrary, large quantities of citation relations are held in
only a few nodes. Particularly, though some nodes with
really small degrees are not accordance with power-law
distribution, their citations are totally rare when
comparing with the entire network scale. To some extent,
this kind of journals is the so-called fringe journals, and it
does not play a vital part on the distribution characteristic
of globe network.
Table 1. The statistical data of fundamental attributes
2003 2004 2005 2006
node number 1577 1659 1658 1787
link number 32823 42909 25923 47470
ratio L/N 20.81357 25.86438 15.6351 26.56407
maximum indegree 211 264 255 288
maximum outdegree 98 84 124 245
average degree 36.27774 44.51718 27.22799 47.6911
network diameter 5 6 8 6
average path length(reachable) 3.47 3.242 4.073 3.782
average path length(bidirectional) 2.709 2.616 2.969 2.642
average clustering coefficient 0.238 0.246 0.269 0.302
Motif-based Classification in Journal Citation Networks 55
Copyright © 2008 SciRes JSEA
Figure 2. The indegree and outdegree distribution
In order to give a further look on the degree characteristic
of these journals, Figure 3 shows the four-year correlations
between indegrees and outdegrees in journal networks, in
which each point corresponds to a node, and the x-position
is determined by the node’s indegree, the y-position
corresponds to its outdegree. We can find that most nodes
in journal network have significant distances with indegree
and outdegree value. They are either with larger indegree
but smaller outdegree, or vice versa. Only few nodes have
both large indegree and outdegree. This characteristic is
especially obvious in the year 2006.
It presents that nodes with large indegree have a good
opportunity to be retrieved by SCI or EI, such typical
examples including Chinese Science Bulletin, Chinese
Journal of Computers, and etc. This kind of journals
usually has a great influence in domestic journals of the
same kind, which lead to a positive citations to them. But
when it refers to their comparatively smaller outdegree,
we believe it has a strong probability these influential
journals prefer to make citations with those international
journals. What have analyzed above indicates one
citation characteristic of Chinese journal networks, that is
journals retrieved by SCI/EI generally have a highly
inclination to be cited, but with low positivity to cite
other non-core journals in contrast.
4. Motif Structure in Journal Citation Networks
4.1 Motif Structure in Communities
It has been mentioned in the previous article that it is
important to research on network local topology structure
and generate mechanisms. In recent years, people find a
clustering characteristic in complex networks [11
Newman proposed the concept of community structure to
indicate that an entire network is comprised of some
communities or clusters. Nodes are joined together in
tightly-knit groups, between which there are only looser
connections. The community structure reflects high
clustering and modularized characteristics. Many real
networks, such as biology network, WWW network and
social network have all been proved had obvious
community structures. This article makes an analysis on
2004 journal citation network, and also finds the typical
community structure in this network.
For the category differences, the citation times between
different kinds of journals are extremely different. For
example, there are only no more than ten times citations
between class of physic and traffic, but thousands of
times citation between all kinds of medical journals, such
as pharmacy, clinical medicine and traditional Chinese
medicine, etc. In principle, tight citation correlations
make journals assemble in the same community, while
loose citation correlations make journals separate into
two communities. Through the designed experiment,
journals of the same category or several similar
categories generally appear in the same community with
the partition of the whole journal network into twenty
different communities in all.
In the following work, this article analyzes the
different citation relations between those different
communities. Motif kind presents in an exploding way
with the increase of node number. For example, there are
13 kinds of motif with three nodes, while the number of
kind rises to 199 with four-node motifs. Since journal
network belongs to sociology field, and it is found that
social networks are more likely to contain triangle
relations. Therefore, in this paper, the research is mainly
outspread on the granularity of three-node motifs.
Figure 3. The indegree and outdegree correlations
56 Motif-based Classification in Journal Citation Networks
Copyright © 2008 SciRes JSEA
According to the concrete meanings in journal citation
networks, these thirteen motifs are classified into two
kinds: one named “unidirectional citation clusters”,
comprising with motif ID36, ID12, ID6, ID38 and ID140.
This kind of motifs have a common characteristic, that is
none of them contains any bidirectional edges, which
means any pairs of nodes in these three-node motifs have
no mutual citation relationships. To be contrast, the other
kind named “mutual citation clusters”, with the motif
members of ID164, ID14, ID78, ID166, ID174, ID46,
ID102 and ID238, in which there could be one or even
more bidirectional edges. In other words, it has at least
one mutual citation relationship between the three nodes.
It indicates in Figure 3 the unidirectional citation
clusters play an absolutely dominant part in journal
networks, proving Chinese journal networks are more
inclined to display unidirectional citation correlations. On
the other hand, the occurrence of mutual citation clusters
is much lower, but their Z-Score [13] values are generally
much higher than motifs belonging to the unidirectional
citation clusters. Z-Score is a certain variable to weigh
the statistical significance in real networks with a comparison
to the corresponding randomized networks. Generally
speaking, the higher Z-Score a motif has, the more
significant for it to present typical characteristics in a
network. Considering in the journal citation network, the
mutual citation clusters’ high Z-Score value can partly
illuminate the mutual citation pattern is a special pattern
occurring in journal networks.
Figure 4 shows motif frequency distribution of partial
communities, according to which we can classify these
communities into two kinds. In the first kind, the motifs
lying in the frontal part of coordinate show a higher
frequency compared to the second kind, while the motifs
lying in the latter part of coordinate have a lower
frequency. The second kind displays in a completely
opposite way. To a further analysis, the first kind
communities are commonly large in node scale, for
example, the Medical Sciences community has 437 nodes;
the Biological and Agricultural community has 184 nodes.
The second kind communities have relatively small node
scale, with only 25 nodes in Light Industry & Textile
community and 37 nodes in Chemical Sciences
Table 3. The Motif Frequencies in Several Network Communities (2004)
Civil & Water 10.62% 12.56% 18.66% 16.45% 14.24% 3.84% 6.10%
Mathematical Sciences 10.20% 10.41% 10.95% 11.82% 12.04% 4.77% 9.76%
Biology & Agriculture 9.68% 26.85% 16.12% 19.26% 8.48% 3.08% 5.97%
Light Industry & Textile 3.55% 9.22% 10.28% 28.37% 9.93% 4.26% 1.06%
Traffic Related 9.24% 11.14% 17.08% 19.97% 14.27% 7.01% 3.80%
Mechanical Engineering 6.38% 16.53% 10.55% 25.48% 9.38% 6.04% 3.72%
Chemical Sciences 6.20% 11.32% 7.91% 22.97% 13.02% 10.02% 2.66%
Electronic Info. & Computer 9.79% 27.90% 15.01% 17.39% 8.35% 2.32% 7.16%
Geological & Geophysical 4.87% 11.99% 8.97% 23.53% 9.54% 7.35% 3.88%
Material Sciences 5.51% 22.65% 9.32% 26.60% 5.63% 5.01% 5.63%
Comprehensive 24.65% 23.27% 30.71% 8.51% 7.10% 0.34% 3.28%
Medical Sciences 14.82% 38.36% 19.29% 11.16% 6.62% 0.92% 4.18%
Physical Sciences 6.17% 12.88% 11.99% 24.34% 10.94% 7.94% 4.06%
Civil & Water 1.00% 3.57% 2.36% 3.89% 5.10% 1.63% 48.92%
Mathematical Sciences 0.98% 6.94% 5.75% 4.45% 9.76% 2.17% 42.30%
Biology & Agriculture 0.38% 2.96% 1.85% 1.79% 2.73% 0.82% 59.01%
Light Industry & Textile 1.16% 7.80% 0.71% 1.06% 11.70%
Traffic Related 0.35% 2.56% 2.48% 2.97% 6.19% 2.15% 41.60%
Mechanical Engineering 0.27% 5.57% 2.16% 2.88% 6.98% 3.98% 37.44%
Chemical Sciences 0.33% 5.04% 2.59% 2.52% 9.41% 6.07% 28.42%
Electronic Info. & Computer 0.59% 4.98% 2.18% 1.18% 2.19% 1.23% 60.44%
Geological & Geophysical 0.06% 6.41% 2.75% 3.86% 9.74% 6.53% 29.77%
Material Science 6.38% 2.32% 2.13% 6.82% 1.94% 0.08% 49.50%
Comprehensive 0.46% 0.17% 0.53% 0.19% 0.57% 0.31% 82.37%
Medical Sciences 0.88% 1.35% 1.14% 0.58% 0.91% 0.51% 77.53%
Physical Sciences 3.88% 3.17% 3.88% 7.05% 2.82% none 38.98%
*UCC means unidirectional citation clusters
Motif-based Classification in Journal Citation Networks 57
Copyright © 2008 SciRes JSEA
Figure 4. The comparison of motif frequencies in communities
Considering with nodes connection principles in the
twenty communities respectively, it is found that in the
first kind of communities, the sum frequencies of motifs
in unidirectional citation clusters exceed 50%, meaning a
dominance of unidirectional citation patterns. A few “hub
nodes” have much larger indegree, and other nodes are
inclined to connect to these nodes. However, these “hub
nodes” always have very few citing connections with
other nodes, even containing in the same community.
For the second kind of communities, the sum value of
motif frequencies belonging to the mutual citation
clusters is more than 50%, making a dominance of
mutual citation pattern. We can see from above analysis
that most nodes in this kind of community play a
common role with no citation inclination in them.
When considering node or edge as the basic
granularity, one characteristic of community structure is
the loose connections between two communities. Then
what characteristics it will show when take three-node
motifs as the basic granularity? For a further
investigation, we also take a research on motif
constitution and citation patterns between these twenty
communities. We find that citation pattern between
communities are entirely inclined to the unidirectional
pattern, meanwhile the frequency of unidirectional
citation clusters is more than 70% between most
communities. This statistical data is even up to 100%
between biology and agriculture community and
electronic information and computer community.
Meanwhile, it is also shown the frequency of the
unidirectional citation clusters between any two
communities is generally much higher than the
corresponding frequency in both two communities. For
example, the electronic information & computer
community and medical community both have an
inclination to unidirectional citation pattern with the
frequency of unidirectional citation cluster 60.44% and
77.53%, respectively. But this frequency rises up to
91.28% between these two communities.
4.2 Node Centrality in Communities
The structure of complex networks is typically
characterized in terms of heterogeneous and topology
differentiate of nodes. Take node centrality in different
communities into consideration. Based on the classical
centrality measures, here this paper mainly discusses
degree centrality and closeness centrality. The former
reflect the numbers of links incident upon a node, while
closeness centrality defines as the reciprocal of geodesic
distance between nodes. Since the lower closeness value
a node has, the higher distance it reaches other nodes,
here we take two typical networks from the two kinds of
communities. One is electronic information & computer
community as the unidirectional citation pattern
community and the light & textile industry community as
the example of mutual citation pattern. Figure 5 shows
the frequency distribution of node centrality in the
electronic information and computer community
It is shown that nodes with large indegrees generally
corresponding to small outdegrees, and the ones with
large outdegrees turn out to have small indegrees. The
Motif Frequency
Biology & Agriculture
Mechanical Engineering
Chemical Sciences
Electronic lnfo. & Computer
Medical Sciences
Physical Sciences
6 36 12 164 14 78 38 140 166 46 102 174 238 0
Motif ID
58 Motif-based Classification in Journal Citation Networks
Copyright © 2008 SciRes JSEA
Figure 5. The centrality on electronic info. & computer communities
electronic information & computer community contains
88 nodes, and there are 19 nodes with indegrees bigger
than 17, in which nearly 70% nodes with outdegrees
smaller than 10. The journal with biggest indegree is
“Computer Engineering and Applications”. Its indegree
value is up to 59, but only has an outdegree value of 14.
To be contrast, “Journal of Beijing University of Posts
and Telecommunications” as the journal with biggest
outdegree of 27, only having an indegree of 5. The
degree distribution characteristic induces a strong
unidirectional citation pattern in this kind of communities.
On the other hand, though the incloseness and outclose-
ness of each node are approximately consistent, the
whole picture shows sharp changes. Most nodes have
small closeness, except four of them, which are
“Computing Techniques for Geophysical and Geo-
chemical Exploration”, “Robots”, “Plezoelectrics and
Acoustooptics” and “Electronic Components & Materials”.
These four nodes all locate near the edge of network, as
shown in Figure 8. left. And their large closenesses
indicate the loose citation relations between them and
other nodes.
In the same way, taking the light & textile industry
community as an example for the second kind of
community to analyze its centrality, and the tendency is
shown in Figure 6. Nodes with large indegrees usually
also have large outdegrees, and vice versa. The node with
maximum in-degree and maximum out-degree all
belongs to “Food Science”, the two values of which don’t
have too much difference (in-degree=11, out-degree=7).
This kind of degree distribution presents tight
connections among the nodes in communities. With
further consideration on closeness centrality, it is easy to
figure out nodes in the light & textile industry distribute
quite even from the globe network, because the closeness
curve displays in a gentle way. Figure 7 gives a directly
look on node closeness, where node sizes are consistent
with their closeness value. This phenomenon tells a
further illustration on the bidirectional citation tendency
of the light & textile industry community.
Figure 6. The centrality on light & textile industry communities
Motif-based Classification in Journal Citation Networks 59
Copyright © 2008 SciRes JSEA
Figure 7. Centrality of journal network communities (left shows the electronic info. & computer community, right
shows the light & textile industry community)
5. Conclusions
Chinese journal citation network is abstracted from more
than one and a half thousands of Chinese journals of
science and technique by CSTPC index. It is found these
networks have obvious clustering characteristic and
small-world pattern. This paper also borrows the motif
concept into consideration to present some structure
differences between two different kinds of network
communities. One kind is more inclined to unidirectional
citation pattern, while the other prefers the bidirectional
citation ones. Then we give a further investigation on the
reason of these two different kinds of citation patterns,
according to node centrality in the communities. With a
detailed statistics on node degree and its closeness, it
illustrates communities of different kind also share
different centrality characteristics.
Unlike general methods, this research takes three-node
motifs as a basic granularity to find the discrepancy
between different communities, rather than on a
traditional node granularity. And it also gets some
interesting ideas on journal citation networks. In the
future, we could probably consider using motifs, a higher
granularity to be a community partition criterion, instead
of only using the system units, node or edge.
6. Acknowledgments
This work is partially supported by the National Grand
Fundamental Research 973 Program of China under
Grant No. 2007CB310803 and the National Natural
Science Foundation of China under Grant No. 60675032.
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