![ACEEE Int. J. on Information Technology, Vol. 02, No. 01, March 2012
Using PageRank Algorithm to Improve Coupling
Metrics
Cheolhyun Park, Junhee Kim, and Eunseok Lee
Department of Electrical and Computer Engineering, Sungkyunkwan University, Suwon, Republic of Korea
Email: {pch851130, comemail, leees}@skku.edu
Abstract—Existing coupling metrics only use the number of II. RELATED WORK AND BACKGROUND
methods invocations, and does not consider the weight of the
methods. Thus, they cannot measure coupling metrics A. Structural Coupling Metrics
accurately. In this paper, we measure the weight of methods Existing coupling metrics only consider the structural
using PageRank algorithm, and propose a new approach to relationship of software. CBO and COF measures coupling
improve coupling metrics using the weight. We validate the using call relationship between classes [3, 4, 5]. RFC measures
proposed approach by applying them to several open source coupling using the number of methods of a class and called
projects. And we measure several coupling metrics using
methods of a class [3, 4]. MPC measures coupling using the
existing approach and proposed approach. As a result, the
correlation between change-proneness and improved coupling number of called methods of a class [6]. DAC measures
metrics were significantly higher than existing coupling coupling using the number of class variables defined in a
metrics. Hence, our improved coupling metrics can more class [6]. In this paper, we improve four coupling metrics
accurately measure software. (CBO, MPC, RFC, and COF). Since these coupling metrics is
directly consider the number of methods invocations, we
Index Terms—software quality metrics, coupling metrics, select these metrics.
PageRank algorithm
B. Semantic Coupling Metrics
I. INTRODUCTION Structural metrics only measures coupling from a data-
flow perspective. Semantic metrics can measure coupling from
Software quality measurement is essential in software
a semantic perspective, such as functional. CoCC (Conceptual
engineering. Coupling of software quality metrics is “the
Coupling of a Class) measures coupling using conceptual
measure of the strength of association established by a
similarity between elements of source code [7]. RTC (Relational
connection from one module to another” [1]. Coupling is
Topic based Coupling) measure coupling using Relational
used for various purposes, such as modularization, reusability,
Topic Models, generative probabilistic to capture latent
fault-proneness, and change-proneness. In this paper, we
topics in source code [8]. Since semantic metrics is only
propose a new approach to improve coupling metrics. Existing
applicable to source code, these are not applicable to artifacts
coupling metrics mainly use the number of method
(i.e., method call graph) in design phase. In this paper, we
invocations [2]. These coupling metrics does not consider
introduce a new approach to improve coupling metrics that
the weight of methods; assume that all methods have same
are applicable to artifacts in design phase.
weight. But since there are any methods that are more
important than other methods, considering the weight of C. PageRank Algorithm
methods is more accurate. In this paper, we measure the weight PageRank is link analysis algorithm that assigns a
of methods using PageRank algorithm, and propose a new numerical weighting to each element of a hyperlinked set of
approach to improve coupling metrics using the weight. We documents, such as the World Wide Web [9]. In this paper,
validate the proposed approach by applying them to several we measure weight of methods using PageRank algorithm.
open source projects. And we measure several coupling Equation (1) shows that calculation method of PageRank
metrics using existing approach and proposed approach. As algorithm.
a result, the correlation between change-proneness and PR(A) = (1-d) + d(PR(T1)/C(T1)+...+PR(Tn)/C(Tn)) (1)
improved coupling metrics were significantly higher than
d = 0.85
existing coupling metrics. We observed that improved
C(Ti) : the number of outbound links on page Ti
coupling metrics could more accurately measure software
quality than existing coupling metrics. The rest of the paper Figure 1 is webpage link graph that is generated randomly.
is organized as follows. Section 2 describes the existing This graph contains the nodes (webpages) and edges (link
coupling metrics; In Section 3, we outline our new approach relationship between webpages). The initial value of
to measure the weight of methods using PageRank algorithm PageRank for each page is assigned to 0.
for improve coupling metrics. Section 4 presents a case study
as an empirical evaluation of the proposed approach. Section
5 concludes the paper and outlines future research.
Figure 1. Webpage link graph
© 2012 ACEEE 56
DOI: 01.IJIT.02.01. 56](https://image.slidesharecdn.com/56-120912225658-phpapp01/85/Using-PageRank-Algorithm-to-Improve-Coupling-Metrics-1-320.jpg)
![ACEEE Int. J. on Information Technology, Vol. 02, No. 01, March 2012
TABLE V. OPEN SOURCE PROJECTS
IV. CASE STUDY
We validate the proposed approach by applying them to
four open source projects. Table 5 gives a description of four
open source project.
A. Experimental Process
1) Java parser generates class information. And we can
measure coupling metrics of each class using created class
information.
2) Then we count the number of changed lines in each
class. And we computed change-proneness using the number
(a) Robocode 1.3 1.7
of changed lines. In this paper, we define change-proneness
as equation (10) that is independent of source code size.
3) Finally, we computed Pearson’s correlation coefficient
between change-proneness and coupling metrics, for each
class. Generally, coupling metrics is used as predictor of the
change-proneness of a class[10, 11, 12]. Therefore, in order
to empirically confirm superiority of improved coupling
metrics, we computed correlation coefficient between change-
proneness and coupling metrics.
(b) JHotDraw 7.1 7.5
B. Experimental Results
We measured four coupling metrics of each class with
existing and proposed approach. And we compute the
correlation coefficient between change-proneness and each
coupling metrics. We show the results of this experiment in
figure 4. In this figure 4, the first bar represents the correlation
coefficient between change-proneness and existing coupling
metrics, and the second bar represents the correlation
coefficient between change-proneness and improved
coupling metrics. In four open source projects, we observed
that the correlation coefficient of all coupling metrics has
been improved. Our improved coupling metrics showed (c) JabRef 1.0 2.7
significantly an improved correlation coefficient as compared
to the existing coupling metrics. Thus, improved coupling
metrics proved to be better predictors than existing coupling
metrics. It can be concluded that improved coupling metrics
is the better metrics.
(d) Heritrix 1.0 1.4
© 2012 ACEEE 58
DOI: 01.IJIT.02.01. 56](https://image.slidesharecdn.com/56-120912225658-phpapp01/85/Using-PageRank-Algorithm-to-Improve-Coupling-Metrics-3-320.jpg)
![ACEEE Int. J. on Information Technology, Vol. 02, No. 01, March 2012
V. CONCLUSION AND FUTURE WORK [5] F. Abreu, M. Goulão, and R. Esteves, “Toward the Design
Quality Evaluation of Object-Oriented Software Systems,” Proc.
In this paper, we measure the weight of methods using Fifth Int’l Conf. Software Quality, Austin, Texas, Oct. 1995.
PageRank algorithm, and proposed a new approach to [6] W. Li and S. Henry, “Object-Oriented Metrics that Predict
improve coupling metrics using the weight. We applied Maintainability,” J. Systems and Software, vol. 23, no. 2, pp. 111-
improved coupling metrics to four open source projects, 122, 1993.
measured the correlation coefficient between change- [7] D. Poshyvanyk and A. Marcus, “The Conceptual Coupling
proneness and coupling metrics, and empirically observed Metrics for Object Oriented Systems,” Proc. 22nd IEEE
superiority of proposed approach. In the future work, we will International Conference on Software Maintenance (ICSM’06),
2006, pp. 469-478.
explore new approach to measure the weight of source code
[8] M. Gethers and D. Poshyvanyk. “Using relational topic
lines, and improve complexity metrics using the weight. models to capture coupling among classes in object-oriented
software systems.” In ICSM’10, 2010.
REFERENCES [9] L. Page, S. Brin, R. Motwani, and T. Winograd, “The PageRank
Citation Ranking: Bringing Order to the Web,” Stanford Digital
[1] W. Stevens, G. Myers, and L. Constantine, “Structured
Libraries Working Paper, 1998.
Design,” IBM Systems J., vol. 13, no. 2, pp. 115-139, 1974.
[10] F. G. Wilkie, B. A. Kitchenham, “Coupling Measures and
[2] L. C. Briand, J. W. Daly, and J. Wüst, “A Unified Framework
Change Ripples in C++ Application Software”, published in the
for Coupling Measurement in Object-Oriented Systems,” IEEE
proceedings of EASE’99, University of Keele, UK, 1998.
Transactions on Software Engineering, vol. 25, pp. 91-121, 1999.
[11] Kagdi H, Gethers M, Poshyvanyk D, Collard M (2010)
[3] S.R. Chidamber and C.F. Kemerer, “Towards a Metrics Suite
“Blending conceptual and evolutionary couplings to support change
for Object Oriented Design,” A. Paepcke, ed., Proc. Conf. Object-
impact analysis in source code”, 17th IEEE Working Conference on
Oriented Programming: Systems, Languages and Applications,
Reverse Engineering (WCRE’10). Boston, USA, 119–128.
OOPSLA’ 91, Oct. 1991. Also published in SIGPLAN Notices,
[12] R. Robbes, D. Pollet, and M. Lanza. “Logical coupling based
vol. 26, no. 11, pp. 197-211, 1991.
on fine-grained change information”, In Proceedings of WCRE 2008
[4] S.R. Chidamber and C.F. Kemerer, “A Metrics Suite for Object
(15th Working Conference on Reverse Engineering), 2008.
Oriented Design,” IEEE Trans. Software Eng., vol. 20, no. 6, pp.
476-493, 1994.
© 2012 ACEEE 59
DOI: 01.IJIT.02.01.56](https://image.slidesharecdn.com/56-120912225658-phpapp01/85/Using-PageRank-Algorithm-to-Improve-Coupling-Metrics-4-320.jpg)
Using PageRank Algorithm to Improve Coupling Metrics
- 1. ACEEE Int. J. on Information Technology, Vol. 02, No. 01, March 2012 Using PageRank Algorithm to Improve Coupling Metrics Cheolhyun Park, Junhee Kim, and Eunseok Lee Department of Electrical and Computer Engineering, Sungkyunkwan University, Suwon, Republic of Korea Email: {pch851130, comemail, leees}@skku.edu Abstract—Existing coupling metrics only use the number of II. RELATED WORK AND BACKGROUND methods invocations, and does not consider the weight of the methods. Thus, they cannot measure coupling metrics A. Structural Coupling Metrics accurately. In this paper, we measure the weight of methods Existing coupling metrics only consider the structural using PageRank algorithm, and propose a new approach to relationship of software. CBO and COF measures coupling improve coupling metrics using the weight. We validate the using call relationship between classes [3, 4, 5]. RFC measures proposed approach by applying them to several open source coupling using the number of methods of a class and called projects. And we measure several coupling metrics using methods of a class [3, 4]. MPC measures coupling using the existing approach and proposed approach. As a result, the correlation between change-proneness and improved coupling number of called methods of a class [6]. DAC measures metrics were significantly higher than existing coupling coupling using the number of class variables defined in a metrics. Hence, our improved coupling metrics can more class [6]. In this paper, we improve four coupling metrics accurately measure software. (CBO, MPC, RFC, and COF). Since these coupling metrics is directly consider the number of methods invocations, we Index Terms—software quality metrics, coupling metrics, select these metrics. PageRank algorithm B. Semantic Coupling Metrics I. INTRODUCTION Structural metrics only measures coupling from a data- flow perspective. Semantic metrics can measure coupling from Software quality measurement is essential in software a semantic perspective, such as functional. CoCC (Conceptual engineering. Coupling of software quality metrics is “the Coupling of a Class) measures coupling using conceptual measure of the strength of association established by a similarity between elements of source code [7]. RTC (Relational connection from one module to another” [1]. Coupling is Topic based Coupling) measure coupling using Relational used for various purposes, such as modularization, reusability, Topic Models, generative probabilistic to capture latent fault-proneness, and change-proneness. In this paper, we topics in source code [8]. Since semantic metrics is only propose a new approach to improve coupling metrics. Existing applicable to source code, these are not applicable to artifacts coupling metrics mainly use the number of method (i.e., method call graph) in design phase. In this paper, we invocations [2]. These coupling metrics does not consider introduce a new approach to improve coupling metrics that the weight of methods; assume that all methods have same are applicable to artifacts in design phase. weight. But since there are any methods that are more important than other methods, considering the weight of C. PageRank Algorithm methods is more accurate. In this paper, we measure the weight PageRank is link analysis algorithm that assigns a of methods using PageRank algorithm, and propose a new numerical weighting to each element of a hyperlinked set of approach to improve coupling metrics using the weight. We documents, such as the World Wide Web [9]. In this paper, validate the proposed approach by applying them to several we measure weight of methods using PageRank algorithm. open source projects. And we measure several coupling Equation (1) shows that calculation method of PageRank metrics using existing approach and proposed approach. As algorithm. a result, the correlation between change-proneness and PR(A) = (1-d) + d(PR(T1)/C(T1)+...+PR(Tn)/C(Tn)) (1) improved coupling metrics were significantly higher than d = 0.85 existing coupling metrics. We observed that improved C(Ti) : the number of outbound links on page Ti coupling metrics could more accurately measure software quality than existing coupling metrics. The rest of the paper Figure 1 is webpage link graph that is generated randomly. is organized as follows. Section 2 describes the existing This graph contains the nodes (webpages) and edges (link coupling metrics; In Section 3, we outline our new approach relationship between webpages). The initial value of to measure the weight of methods using PageRank algorithm PageRank for each page is assigned to 0. for improve coupling metrics. Section 4 presents a case study as an empirical evaluation of the proposed approach. Section 5 concludes the paper and outlines future research. Figure 1. Webpage link graph © 2012 ACEEE 56 DOI: 01.IJIT.02.01. 56
- 2. ACEEE Int. J. on Information Technology, Vol. 02, No. 01, March 2012 Since the calculation is an iterative process, the algorithm is stopped after a given count of iterations or if the PageRank value differences between iterations are less than predefined values. TABLE I. R ESULTS OF PAGERANK ALGORITHM Figure 3. Class call graph Table 4 shows that weight of three classes were computed based on PageRank algorithm. As mentioned above, we can measure weight of methods and classes using PageRank algorithm. III. PROPOSED APPROACH TABLE IV. WEIGHT OF CLASSES In this section, we measure the weight of methods using PageRank algorithm, and improve four coupling metrics using the measured weight of methods. A. Measurement of Methods Weight A. Improvement of Coupling Metrics In order to measure coupling metrics, figure 2 is method In this section, coupling metrics can be described by call graph generated randomly. This graph consists of following equations. When we use suffix ‘N’ in each metrics, nodes(methods) and edges(call relationship between it means improved cohesion metrics. methods). 1) CBO : The set of called classes of class ‘c’ : PageRank of class ‘c’ 2) MPC Figure 2. Method call graph We applied Pagerank algorithm to this method call graph. Table 2 shows that weight of five methods were computed based on PageRank algorithm. : The set of called methods of class ‘c’ TABLE II. WEIGHT OF METHODS : PageRank of method ‘m’ 3) RFC Table 3 shows methods of each class. We can construct class call graph using Figure2 and Table 3. Figure 3 shows class call graph. : The number of methods of class ‘c’ TABLE III. METHODS OF EACH CLASS 4) CFO : The number of all classes © 2012 ACEEE 57 DOI: 01.IJIT.02.01.56
- 3. ACEEE Int. J. on Information Technology, Vol. 02, No. 01, March 2012 TABLE V. OPEN SOURCE PROJECTS IV. CASE STUDY We validate the proposed approach by applying them to four open source projects. Table 5 gives a description of four open source project. A. Experimental Process 1) Java parser generates class information. And we can measure coupling metrics of each class using created class information. 2) Then we count the number of changed lines in each class. And we computed change-proneness using the number (a) Robocode 1.3 1.7 of changed lines. In this paper, we define change-proneness as equation (10) that is independent of source code size. 3) Finally, we computed Pearson’s correlation coefficient between change-proneness and coupling metrics, for each class. Generally, coupling metrics is used as predictor of the change-proneness of a class[10, 11, 12]. Therefore, in order to empirically confirm superiority of improved coupling metrics, we computed correlation coefficient between change- proneness and coupling metrics. (b) JHotDraw 7.1 7.5 B. Experimental Results We measured four coupling metrics of each class with existing and proposed approach. And we compute the correlation coefficient between change-proneness and each coupling metrics. We show the results of this experiment in figure 4. In this figure 4, the first bar represents the correlation coefficient between change-proneness and existing coupling metrics, and the second bar represents the correlation coefficient between change-proneness and improved coupling metrics. In four open source projects, we observed that the correlation coefficient of all coupling metrics has been improved. Our improved coupling metrics showed (c) JabRef 1.0 2.7 significantly an improved correlation coefficient as compared to the existing coupling metrics. Thus, improved coupling metrics proved to be better predictors than existing coupling metrics. It can be concluded that improved coupling metrics is the better metrics. (d) Heritrix 1.0 1.4 © 2012 ACEEE 58 DOI: 01.IJIT.02.01. 56
- 4. ACEEE Int. J. on Information Technology, Vol. 02, No. 01, March 2012 V. CONCLUSION AND FUTURE WORK [5] F. Abreu, M. Goulão, and R. Esteves, “Toward the Design Quality Evaluation of Object-Oriented Software Systems,” Proc. In this paper, we measure the weight of methods using Fifth Int’l Conf. Software Quality, Austin, Texas, Oct. 1995. PageRank algorithm, and proposed a new approach to [6] W. Li and S. Henry, “Object-Oriented Metrics that Predict improve coupling metrics using the weight. We applied Maintainability,” J. Systems and Software, vol. 23, no. 2, pp. 111- improved coupling metrics to four open source projects, 122, 1993. measured the correlation coefficient between change- [7] D. Poshyvanyk and A. Marcus, “The Conceptual Coupling proneness and coupling metrics, and empirically observed Metrics for Object Oriented Systems,” Proc. 22nd IEEE superiority of proposed approach. In the future work, we will International Conference on Software Maintenance (ICSM’06), 2006, pp. 469-478. explore new approach to measure the weight of source code [8] M. Gethers and D. Poshyvanyk. “Using relational topic lines, and improve complexity metrics using the weight. models to capture coupling among classes in object-oriented software systems.” In ICSM’10, 2010. REFERENCES [9] L. Page, S. Brin, R. Motwani, and T. Winograd, “The PageRank Citation Ranking: Bringing Order to the Web,” Stanford Digital [1] W. Stevens, G. Myers, and L. Constantine, “Structured Libraries Working Paper, 1998. Design,” IBM Systems J., vol. 13, no. 2, pp. 115-139, 1974. [10] F. G. Wilkie, B. A. Kitchenham, “Coupling Measures and [2] L. C. Briand, J. W. Daly, and J. Wüst, “A Unified Framework Change Ripples in C++ Application Software”, published in the for Coupling Measurement in Object-Oriented Systems,” IEEE proceedings of EASE’99, University of Keele, UK, 1998. Transactions on Software Engineering, vol. 25, pp. 91-121, 1999. [11] Kagdi H, Gethers M, Poshyvanyk D, Collard M (2010) [3] S.R. Chidamber and C.F. Kemerer, “Towards a Metrics Suite “Blending conceptual and evolutionary couplings to support change for Object Oriented Design,” A. Paepcke, ed., Proc. Conf. Object- impact analysis in source code”, 17th IEEE Working Conference on Oriented Programming: Systems, Languages and Applications, Reverse Engineering (WCRE’10). Boston, USA, 119–128. OOPSLA’ 91, Oct. 1991. Also published in SIGPLAN Notices, [12] R. Robbes, D. Pollet, and M. Lanza. “Logical coupling based vol. 26, no. 11, pp. 197-211, 1991. on fine-grained change information”, In Proceedings of WCRE 2008 [4] S.R. Chidamber and C.F. Kemerer, “A Metrics Suite for Object (15th Working Conference on Reverse Engineering), 2008. Oriented Design,” IEEE Trans. Software Eng., vol. 20, no. 6, pp. 476-493, 1994. © 2012 ACEEE 59 DOI: 01.IJIT.02.01.56