Applying Complex Network Theory to Software Structure Analysis
Complex networks have been intensively studied across
many fields, especially in Internet technology, biological engineering,
and nonlinear science. Software is built up out of many interacting
components at various levels of granularity, such as functions, classes,
and packages, representing another important class of complex networks.
It can also be studied using complex network theory. Over the
last decade, many papers on the interdisciplinary research between
software engineering and complex networks have been published.
It provides a different dimension to our understanding of software
and also is very useful for the design and development of software
systems. This paper will explore how to use the complex network
theory to analyze software structure, and briefly review the main
advances in corresponding aspects.
[1] W. Pan, Software Networks-Based Analysis of Software Static Structure
and Its Applications. Wuhan: Wuhan University, 2011.
[2] W. Pan, B. Li, Y. Ma, Y. Qin, and X. Zhou, "Measuring Structural Quality
of Object-Oriented Softwares via Bug Propagation Analysis on Weighted
Software Networks", Journal of Computer Science and Technology, vol.
25, no. 6, pp. 1202-1213, 2010.
[3] L. Costa, O. Oliveria, and G. Travieso, "Analyzing and Modeling Real-
World Phenomena with Complex Networks: a Survey of Applications",
arXiv:0711.3199v2, 2008.
[4] J. L¨u and G. Chen, "Analysis, Control and Application of Complex
Networks: a Brief Overview", Pro. of the 2009 IEEE International
Symposium on Circuits and Systems, pp. 1601-1604, 2009.
[5] J. L¨u and D. Liu, "A Brief Overview of the Complex Biological and
Engineering Networks", Pro. of the 2007 IEEE International Symposium
on Circuits and Systems, pp. 2634-2637, 2007.
[6] W. Pan, B. Li, Y. Ma, and Jing Liu, "Multi-Granularity Evolution Analysis
of Software using Complex Network Theory", Journal of Systems Science
and Complexity, vol. 24, pp. 1-15, 2011.
[7] W. Pan, B. Li, Y. Ma, J. Liu, and Y. Qin, "Class Structure Refactoring of
Object-Oriented Softwares using Coommunity Detection in Dependency
Networks", Frontiers of Computer Science in China, vol. 3, no. 3, pp.
396-404, 2009,
[8] R. W. Wolverton, "The Cost of Developing Large-Scale Software", IEEE
Transactions on Computers, vol. C-23, no. 6, pp. 615-636.
[9] T. J. McCabe, "A Complexity Measure", IEEE Transactions on Software
Engineering, vol. SE-2, no. 4, pp. 308-320, 1976.
[10] M. H. Halstead, "Elements of Software Science", Operating, and
Programming Systems, vol. 7, pp. 128, 1977.
[11] B. H. Yin and J. W. Winchester, "The Establishment and Use of
Measures to Evaluate the Quality of Software Designs", Software quality
assurance workshop on Functional and performance, pp. 45-52, 1978.
[12] C. L. McClure, "A Model for Program Complexity Analysis", Proc. of
the 3rd International Conference on Software Engineering, pp. 149-157,
1978.
[13] N. Woodfield, "Enhanced Effort Estimation by Extending Basic Programming
Models to Include Modularity Factors", West-Lafayette, USA,
1980.
[14] S. Henry and D. Kafura, "Software Structure Metrics Based on Information
Flow", IEEE Transactions on Software Engineering, pp. 510-518,
1981.
[15] K. C. Tai, "A Program Complexity metric based on Data Flow Information
in Control Graphs", Proc. of the 7th International Conference on
Software Engineering, pp. 239-248, 1984.
[16] B. F. Abreu and R. Carapuca, "Candidate Metrics for Object-Oriented
Software within a Taxonomy Framework", Journal of systems software,
vol. 26, no. 1, pp. 87-96, 1994.
[17] S. R. Chidamber and C. F. Kemerer, "A Metrics Suite for Object-
Oriented Design", IEEE Transactions on Software Engineering, vol. 20,
no. 6, pp. 476-493, 1994.
[18] W. Li and S. Henry, "Object-Oriented Metrics that Predict Maintainability",
Journal Of Systems And Software, vol. 23, no. 2, pp. 111-122,
1993.
[19] F. B. Abreu, "The MOOD Metrics Set", Proc. of the ECOOP95
Workshop on Metrics, 1995.
[20] F. B. Abreu, "Design Metrics for OO Software System", Proc. of the
ECOOP95 Quantitative Methods Workshop, 1995.
[21] M. Lorenz and J. Kidd, Object-Oriented Software Metrics: a Practical
Guide. NJ: Prentice Hall PTR, 1994.
[22] R. Subramanyan and M. S. Krishnan, "Empirical Analysis of CK Metrics
for Object-Oriented Design Complexity: Implications for Software
Defects", IEEE Transactions on Software Engineering, vol. 29, no. 10,
pp. 297-310, 2003.
[23] V. R. Basili, L. C. Briand, and W. L. Melo, "A Validation of Object-
Oriented Design Metrics as Quality Indicators", IEEE Transactions on
Software Engineering, vol. 22, no. 10, pp. 751-761, 1996.
[24] K. EI Emam, S. Benlarbi, N. Goel, "The Confounding Effect of Class
Size on the Validity of Object-Oriented Metrics", IEEE Transactions on
Software Engineering, vol. 27, no. 6, pp. 630-650, 2001.
[25] T. Gyim'othy, R. Ferenc, and I. Siket, "Empirical Validation of Object-
Oriented Metrics on Open Source Software for Fault Prediction", IEEE
Transactions on Software Engineering, vol. 31, no. 10, pp. 897-910, 2003.
[26] B. Zhang, "Network and Complex Systems", Scientific Chinese, vol. 10,
pp. 37-37, 2004.
[27] G. Chen, "Introduction to Complex Networks and Their Recent
Advances", Advances in Mechanics, vol. 38, no. 6, pp. 653-662, 2008.
[28] D. J. Watts and S. H. Strogatz, "Collective Dynamics of Small World
Networks", Nature, vol. 393, pp. 440-442, 1998.
[29] A. L. Barab'asi and R. Albert, "Emergence of Scaling in Random
Networks", Science, vol. 286, pp. 509-512, 1999.
[30] Committee on Network Science for Future Army Application, Network
Science, Washington DC: National Academies Press, 2006.
[31] A. L. Barab'asi, Linked: the New Science of Networks, Cambridge MA:
Perseus Publishing, 2002.
[32] D. J. Watts, "The "new" Science of Networks", Annual Review of
Sociology, vol, 30, pp. 243-270, 2004.
[33] M. Faloutsos, P. Faloutsos, and C. Faloutsos, "On power-law Relationships
of The Internet Topology", Computer Communication Review, vol.
29, no. 4, pp. 251- 262, 1999.
[34] G. Siganos, M. Faloutsos, P. Faloutsos, et al., "Power Laws and The
AS-Level Internet Topology", IEEE/ACM Transactions on Networking,
vol. 11, no. 4, pp. 514-524, 2003.
[35] L. A. Adamic and B. A. Huberman, "Power-Law Distribution of The
World Wide Web", Science, vol. 287, pp. 2115a, 2000.
[36] R. Guimer`a, S. Mossa, A. Turtschi, et al., "The Worldwide Air Transportation
Network: Anomalous Centrality, Community Structure, and
Cities- Global Roles", Proceedings of the National Academy of Science
USA, vol. 102, pp. 3394-7799, 2005.
[37] W. Li and X. Cai, "Statistical Analysis of Airport Network of China",
Physical Review E, vol. 68, no. 4: 46106, 2004, .
[38] O. Sporns, "Network Analysis, Complexity, and Brain Function", Complexity,
vol. 8, no. 1, pp. 56-60, 2002.
[39] H. Jeong, B. Tombor, R. Albert, et al., "The Large-Scale Organizationn
of Metabolic Networks", Nature, vol. 407, pp. 651-654, 2000.
[40] M. E. J. Newman, "Scientific Collaboration Networks. I. Network
Construction and Fundamental Results", Physical Review E, vol. 64, no.
1, pp. 16131, 2001.
[41] M. A. Serrano and M. Bogu˜n'a, "Topology of The World Trade Web",
Physical Review E, vol. 68, pp. 015101, 2003.
[42] A. E. Motter, A. P. S. Moura, Y. C. Lai, et al., "Topology of The
Conceptual Network of Language", Physical Review E, vol. 65, pp.
065102, 2002.
[43] G. Corso, "Families and Clustering in a Natural Numbers Network",
Physical Review E, vol. 60, no. 3, pp. 036106-036110, 2004.
[44] X. Liu, C. K. Tse, and M. Small, "Complex Network Structure of
Musical Compositions: Algorithmic Generation of Appealing Music",
Physica A, vol. 389, no. 1, pp. 126-132, 2010.
[45] S. Abe and N. Suzuki, "Scale-Free Network of Earthquakes", Europhysics
Letters, vol. 65, no. 4, pp. 581-586, 2004.
[46] S. Valverde, R. F. i Cancho, and R. Sole, "Scale Free Networks from
Optimal Design", Europhysics Letters, vo. 60, pp. 512-517, 2002.
[47] C. R. Myers, "Software Systems as Complex Networks: Structure,
Function, and Evolvability of Software Collaboration Graphs, Physical
Review E, vol. 68, 2003.
[48] S. Valverde and R. Sol'e, "Hierarchical Small Worlds in Software
Architecture", Working Paper of Santa Fe Institue, SFI/03-07-44, 2003.
[49] A. P. S. Moura, Y. C. Lai, and A. E. Motter, "Signatures of Small-World
and Scale-Free Properties in Large Computer Programs", Physical Review
E, vol. 68, pp. 017102, 2003.
[50] N. LaBelle and E. Wallingford, "Inter-Package Dependency Networks
in Open-Source Software", ArXiv: Cs.SE/0411096, 2004.
[51] S. Valverde and R. V. Sole, "Universal Properties of Bipartite Software
Graphs", Proc. of the 9th IEEE International Conference on Engineering
of Complex Computer Systems, 2004.
[52] M. Han, D. Li, C. Liu, et al. "Networked Characteristics in Software
and its Contribution to Software Quality", Computer Engineering and
Application, vol. 42, no. 20, pp. 29-31, 2006. (in Chinese)
[53] J. Liu, K. He, Y. Ma, et al., "Scale Free in Software Metrics", Proc.
of the 30th Annual International Computer Software and Application
Conference, pp. 229-235, 2004.
[54] J. Liu, K. He, R. Peng, et al., "A Study on the Weight and Topology
Correlation of Object-Oriented Software Coupling Network", Proc. of the
1st International Conference on Complex Systems and Applications, PP.
955-959, 2006.
[55] D. Yan, G. QI, "The Scale-free Feature and Evolving Model of Large-
Scale Software systems", Acta Phisica Sinica, vol. 55, no. 8, pp. 3799-
3084, 2006.
[56] H. Zhang, H. Zhao, W. Cai, et al., "Using the k-core Decomposition
to Analyze the Static Structure of Large-Scale Software Systems", The
Journal of Supercomputing, vol. 53, no. 2, pp. 352-369, 2010.
[57] S. Jenkins and S. R. Kirk, "Software Architecture Graphs as Complex
Networks: a Novel Parttion Scheme to Measure Stability and Evolution",
Information Sciences, vol. 177, no. 12, pp. 2587-2601, 2007.
[58] M. Shi, X. Li, and X. Wang, "Evolving Topology of Java Networks",
Proc. of the 6th World Congress on Control and Automation, PP. 21-23,
2006.
[59] L. Wang, Z. Wang, C. Yang, et al., "Linux Kernels as Complex
Networks: a Novel Method to Study Evolution", Proc. of the 25th
International Conference on Software Maintenance, PP. 41-50, 2009.
[60] H. Li, B. Huang, and J. Lu, "Dynamical Evolution Analysis of the
Object-Oriented Software Systems", Proc. of the 2008 IEEE World
Congress on Computational Intelligence, PP. 3035-3040, 2008.
[61] R. V. Sole and S. Valverde, "Information Theory of Complex Networks:
on Evolution and Architectural Constraints", Proc. of the International
Conference on Complex Networks, pp. 189-207, 2004.
[62] S. Valverde and R. V. Sole, "Network Motifs in Computational Graphs:
a Case Study in Software Architecture", Physical Review E, vol. 72, pp.
026107, 2005.
[63] K. He, R. Peng, J. Liu, et al., "Network Motifs in Computational Graphs:
a Case Study in Software Architecture", Journal of Systems Science and
Complexity, vol. 19, no. 2, pp. 157-181, 2006.
[64] B. Li, H. Wang, Z. Li, et al., "Software Complexity Metrics Based on
Complex Networks", Acta Electronica Sinica, vol. 34, no. 12A, pp. 2371-
2375, 2006. (in Chinese).
[65] H. Li, "Scale-Free Network Models with Accelerating Growth", Frontier
of Computer Science in China, vol. 3, no. 3, pp. 373-380, 2009.
[66] W. Pan, B. Li, Y. Ma, and J. Liu, "A Novel Software Evolution Model
Based on Software Networks", Complex (2), 1281-1291, 2009.
[67] R. Vasa, J. G. Schneider, C. Woodward, et al., Detecting Structural
Changes in Object Oriented Software Systems, Proc. of the International
Symposium on Empirical Software Engineering, PP. 479-486, 2005.
[68] Y. Ma, K. He, and D. Du, "A Qualitative Method for Measuring the
Structural Complexity of Software Systems based on Complex Networks",
Proc. of the 12th Asia-Pacific Software Engineering Conference,
PP. 257-263, 2005.
[69] A. Girolamo, L. I. Newman, and R. Rao, "The Structure and
Behavior of Class Networks in Object-Oriented Software Design",
www.eecs.umich.edu/ leenewm/ documents/classnetworks.pdf, 2005.
[70] Y. Ma, K. He, D. Du, et al., "A Complexity Metrics Set for Large-
Scale Object-Oriented Software Systems", Proc. of the 6th International
Conference on Computer and Information Technology, PP. 257-263, 2006.
[71] R. Vasa, J. G. Schneider, and O. Nierstrasz, "The Inevitable Stability of
Software Change", Proc. of the 23nd IEEE International Conference on
Software Maintenance, Paris France, PP. 4-13, 2007.
[72] H. Melton and E. Tempero, "Static Members and Cycles in Java Software",
Proc. of the 1st International Symposium on Empirical Software
Engineering and Measurement, PP. 136-145, 2007.
[73] Y. Ma, K. He, and J. Liu, "Network Motifs in Object-Oriented Software
Systems", Dynamics of Continuous, Discrete and Impulsive System
(Series B: Applications and Algorithms) Special Issue on Software Engineering
and Complex Networks, vol. 16, no. S6, pp. 166-172, 2007.
[1] W. Pan, Software Networks-Based Analysis of Software Static Structure
and Its Applications. Wuhan: Wuhan University, 2011.
[2] W. Pan, B. Li, Y. Ma, Y. Qin, and X. Zhou, "Measuring Structural Quality
of Object-Oriented Softwares via Bug Propagation Analysis on Weighted
Software Networks", Journal of Computer Science and Technology, vol.
25, no. 6, pp. 1202-1213, 2010.
[3] L. Costa, O. Oliveria, and G. Travieso, "Analyzing and Modeling Real-
World Phenomena with Complex Networks: a Survey of Applications",
arXiv:0711.3199v2, 2008.
[4] J. L¨u and G. Chen, "Analysis, Control and Application of Complex
Networks: a Brief Overview", Pro. of the 2009 IEEE International
Symposium on Circuits and Systems, pp. 1601-1604, 2009.
[5] J. L¨u and D. Liu, "A Brief Overview of the Complex Biological and
Engineering Networks", Pro. of the 2007 IEEE International Symposium
on Circuits and Systems, pp. 2634-2637, 2007.
[6] W. Pan, B. Li, Y. Ma, and Jing Liu, "Multi-Granularity Evolution Analysis
of Software using Complex Network Theory", Journal of Systems Science
and Complexity, vol. 24, pp. 1-15, 2011.
[7] W. Pan, B. Li, Y. Ma, J. Liu, and Y. Qin, "Class Structure Refactoring of
Object-Oriented Softwares using Coommunity Detection in Dependency
Networks", Frontiers of Computer Science in China, vol. 3, no. 3, pp.
396-404, 2009,
[8] R. W. Wolverton, "The Cost of Developing Large-Scale Software", IEEE
Transactions on Computers, vol. C-23, no. 6, pp. 615-636.
[9] T. J. McCabe, "A Complexity Measure", IEEE Transactions on Software
Engineering, vol. SE-2, no. 4, pp. 308-320, 1976.
[10] M. H. Halstead, "Elements of Software Science", Operating, and
Programming Systems, vol. 7, pp. 128, 1977.
[11] B. H. Yin and J. W. Winchester, "The Establishment and Use of
Measures to Evaluate the Quality of Software Designs", Software quality
assurance workshop on Functional and performance, pp. 45-52, 1978.
[12] C. L. McClure, "A Model for Program Complexity Analysis", Proc. of
the 3rd International Conference on Software Engineering, pp. 149-157,
1978.
[13] N. Woodfield, "Enhanced Effort Estimation by Extending Basic Programming
Models to Include Modularity Factors", West-Lafayette, USA,
1980.
[14] S. Henry and D. Kafura, "Software Structure Metrics Based on Information
Flow", IEEE Transactions on Software Engineering, pp. 510-518,
1981.
[15] K. C. Tai, "A Program Complexity metric based on Data Flow Information
in Control Graphs", Proc. of the 7th International Conference on
Software Engineering, pp. 239-248, 1984.
[16] B. F. Abreu and R. Carapuca, "Candidate Metrics for Object-Oriented
Software within a Taxonomy Framework", Journal of systems software,
vol. 26, no. 1, pp. 87-96, 1994.
[17] S. R. Chidamber and C. F. Kemerer, "A Metrics Suite for Object-
Oriented Design", IEEE Transactions on Software Engineering, vol. 20,
no. 6, pp. 476-493, 1994.
[18] W. Li and S. Henry, "Object-Oriented Metrics that Predict Maintainability",
Journal Of Systems And Software, vol. 23, no. 2, pp. 111-122,
1993.
[19] F. B. Abreu, "The MOOD Metrics Set", Proc. of the ECOOP95
Workshop on Metrics, 1995.
[20] F. B. Abreu, "Design Metrics for OO Software System", Proc. of the
ECOOP95 Quantitative Methods Workshop, 1995.
[21] M. Lorenz and J. Kidd, Object-Oriented Software Metrics: a Practical
Guide. NJ: Prentice Hall PTR, 1994.
[22] R. Subramanyan and M. S. Krishnan, "Empirical Analysis of CK Metrics
for Object-Oriented Design Complexity: Implications for Software
Defects", IEEE Transactions on Software Engineering, vol. 29, no. 10,
pp. 297-310, 2003.
[23] V. R. Basili, L. C. Briand, and W. L. Melo, "A Validation of Object-
Oriented Design Metrics as Quality Indicators", IEEE Transactions on
Software Engineering, vol. 22, no. 10, pp. 751-761, 1996.
[24] K. EI Emam, S. Benlarbi, N. Goel, "The Confounding Effect of Class
Size on the Validity of Object-Oriented Metrics", IEEE Transactions on
Software Engineering, vol. 27, no. 6, pp. 630-650, 2001.
[25] T. Gyim'othy, R. Ferenc, and I. Siket, "Empirical Validation of Object-
Oriented Metrics on Open Source Software for Fault Prediction", IEEE
Transactions on Software Engineering, vol. 31, no. 10, pp. 897-910, 2003.
[26] B. Zhang, "Network and Complex Systems", Scientific Chinese, vol. 10,
pp. 37-37, 2004.
[27] G. Chen, "Introduction to Complex Networks and Their Recent
Advances", Advances in Mechanics, vol. 38, no. 6, pp. 653-662, 2008.
[28] D. J. Watts and S. H. Strogatz, "Collective Dynamics of Small World
Networks", Nature, vol. 393, pp. 440-442, 1998.
[29] A. L. Barab'asi and R. Albert, "Emergence of Scaling in Random
Networks", Science, vol. 286, pp. 509-512, 1999.
[30] Committee on Network Science for Future Army Application, Network
Science, Washington DC: National Academies Press, 2006.
[31] A. L. Barab'asi, Linked: the New Science of Networks, Cambridge MA:
Perseus Publishing, 2002.
[32] D. J. Watts, "The "new" Science of Networks", Annual Review of
Sociology, vol, 30, pp. 243-270, 2004.
[33] M. Faloutsos, P. Faloutsos, and C. Faloutsos, "On power-law Relationships
of The Internet Topology", Computer Communication Review, vol.
29, no. 4, pp. 251- 262, 1999.
[34] G. Siganos, M. Faloutsos, P. Faloutsos, et al., "Power Laws and The
AS-Level Internet Topology", IEEE/ACM Transactions on Networking,
vol. 11, no. 4, pp. 514-524, 2003.
[35] L. A. Adamic and B. A. Huberman, "Power-Law Distribution of The
World Wide Web", Science, vol. 287, pp. 2115a, 2000.
[36] R. Guimer`a, S. Mossa, A. Turtschi, et al., "The Worldwide Air Transportation
Network: Anomalous Centrality, Community Structure, and
Cities- Global Roles", Proceedings of the National Academy of Science
USA, vol. 102, pp. 3394-7799, 2005.
[37] W. Li and X. Cai, "Statistical Analysis of Airport Network of China",
Physical Review E, vol. 68, no. 4: 46106, 2004, .
[38] O. Sporns, "Network Analysis, Complexity, and Brain Function", Complexity,
vol. 8, no. 1, pp. 56-60, 2002.
[39] H. Jeong, B. Tombor, R. Albert, et al., "The Large-Scale Organizationn
of Metabolic Networks", Nature, vol. 407, pp. 651-654, 2000.
[40] M. E. J. Newman, "Scientific Collaboration Networks. I. Network
Construction and Fundamental Results", Physical Review E, vol. 64, no.
1, pp. 16131, 2001.
[41] M. A. Serrano and M. Bogu˜n'a, "Topology of The World Trade Web",
Physical Review E, vol. 68, pp. 015101, 2003.
[42] A. E. Motter, A. P. S. Moura, Y. C. Lai, et al., "Topology of The
Conceptual Network of Language", Physical Review E, vol. 65, pp.
065102, 2002.
[43] G. Corso, "Families and Clustering in a Natural Numbers Network",
Physical Review E, vol. 60, no. 3, pp. 036106-036110, 2004.
[44] X. Liu, C. K. Tse, and M. Small, "Complex Network Structure of
Musical Compositions: Algorithmic Generation of Appealing Music",
Physica A, vol. 389, no. 1, pp. 126-132, 2010.
[45] S. Abe and N. Suzuki, "Scale-Free Network of Earthquakes", Europhysics
Letters, vol. 65, no. 4, pp. 581-586, 2004.
[46] S. Valverde, R. F. i Cancho, and R. Sole, "Scale Free Networks from
Optimal Design", Europhysics Letters, vo. 60, pp. 512-517, 2002.
[47] C. R. Myers, "Software Systems as Complex Networks: Structure,
Function, and Evolvability of Software Collaboration Graphs, Physical
Review E, vol. 68, 2003.
[48] S. Valverde and R. Sol'e, "Hierarchical Small Worlds in Software
Architecture", Working Paper of Santa Fe Institue, SFI/03-07-44, 2003.
[49] A. P. S. Moura, Y. C. Lai, and A. E. Motter, "Signatures of Small-World
and Scale-Free Properties in Large Computer Programs", Physical Review
E, vol. 68, pp. 017102, 2003.
[50] N. LaBelle and E. Wallingford, "Inter-Package Dependency Networks
in Open-Source Software", ArXiv: Cs.SE/0411096, 2004.
[51] S. Valverde and R. V. Sole, "Universal Properties of Bipartite Software
Graphs", Proc. of the 9th IEEE International Conference on Engineering
of Complex Computer Systems, 2004.
[52] M. Han, D. Li, C. Liu, et al. "Networked Characteristics in Software
and its Contribution to Software Quality", Computer Engineering and
Application, vol. 42, no. 20, pp. 29-31, 2006. (in Chinese)
[53] J. Liu, K. He, Y. Ma, et al., "Scale Free in Software Metrics", Proc.
of the 30th Annual International Computer Software and Application
Conference, pp. 229-235, 2004.
[54] J. Liu, K. He, R. Peng, et al., "A Study on the Weight and Topology
Correlation of Object-Oriented Software Coupling Network", Proc. of the
1st International Conference on Complex Systems and Applications, PP.
955-959, 2006.
[55] D. Yan, G. QI, "The Scale-free Feature and Evolving Model of Large-
Scale Software systems", Acta Phisica Sinica, vol. 55, no. 8, pp. 3799-
3084, 2006.
[56] H. Zhang, H. Zhao, W. Cai, et al., "Using the k-core Decomposition
to Analyze the Static Structure of Large-Scale Software Systems", The
Journal of Supercomputing, vol. 53, no. 2, pp. 352-369, 2010.
[57] S. Jenkins and S. R. Kirk, "Software Architecture Graphs as Complex
Networks: a Novel Parttion Scheme to Measure Stability and Evolution",
Information Sciences, vol. 177, no. 12, pp. 2587-2601, 2007.
[58] M. Shi, X. Li, and X. Wang, "Evolving Topology of Java Networks",
Proc. of the 6th World Congress on Control and Automation, PP. 21-23,
2006.
[59] L. Wang, Z. Wang, C. Yang, et al., "Linux Kernels as Complex
Networks: a Novel Method to Study Evolution", Proc. of the 25th
International Conference on Software Maintenance, PP. 41-50, 2009.
[60] H. Li, B. Huang, and J. Lu, "Dynamical Evolution Analysis of the
Object-Oriented Software Systems", Proc. of the 2008 IEEE World
Congress on Computational Intelligence, PP. 3035-3040, 2008.
[61] R. V. Sole and S. Valverde, "Information Theory of Complex Networks:
on Evolution and Architectural Constraints", Proc. of the International
Conference on Complex Networks, pp. 189-207, 2004.
[62] S. Valverde and R. V. Sole, "Network Motifs in Computational Graphs:
a Case Study in Software Architecture", Physical Review E, vol. 72, pp.
026107, 2005.
[63] K. He, R. Peng, J. Liu, et al., "Network Motifs in Computational Graphs:
a Case Study in Software Architecture", Journal of Systems Science and
Complexity, vol. 19, no. 2, pp. 157-181, 2006.
[64] B. Li, H. Wang, Z. Li, et al., "Software Complexity Metrics Based on
Complex Networks", Acta Electronica Sinica, vol. 34, no. 12A, pp. 2371-
2375, 2006. (in Chinese).
[65] H. Li, "Scale-Free Network Models with Accelerating Growth", Frontier
of Computer Science in China, vol. 3, no. 3, pp. 373-380, 2009.
[66] W. Pan, B. Li, Y. Ma, and J. Liu, "A Novel Software Evolution Model
Based on Software Networks", Complex (2), 1281-1291, 2009.
[67] R. Vasa, J. G. Schneider, C. Woodward, et al., Detecting Structural
Changes in Object Oriented Software Systems, Proc. of the International
Symposium on Empirical Software Engineering, PP. 479-486, 2005.
[68] Y. Ma, K. He, and D. Du, "A Qualitative Method for Measuring the
Structural Complexity of Software Systems based on Complex Networks",
Proc. of the 12th Asia-Pacific Software Engineering Conference,
PP. 257-263, 2005.
[69] A. Girolamo, L. I. Newman, and R. Rao, "The Structure and
Behavior of Class Networks in Object-Oriented Software Design",
www.eecs.umich.edu/ leenewm/ documents/classnetworks.pdf, 2005.
[70] Y. Ma, K. He, D. Du, et al., "A Complexity Metrics Set for Large-
Scale Object-Oriented Software Systems", Proc. of the 6th International
Conference on Computer and Information Technology, PP. 257-263, 2006.
[71] R. Vasa, J. G. Schneider, and O. Nierstrasz, "The Inevitable Stability of
Software Change", Proc. of the 23nd IEEE International Conference on
Software Maintenance, Paris France, PP. 4-13, 2007.
[72] H. Melton and E. Tempero, "Static Members and Cycles in Java Software",
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@article{"International Journal of Information, Control and Computer Sciences:56018", author = "Weifeng Pan", title = "Applying Complex Network Theory to Software Structure Analysis", abstract = "Complex networks have been intensively studied across
many fields, especially in Internet technology, biological engineering,
and nonlinear science. Software is built up out of many interacting
components at various levels of granularity, such as functions, classes,
and packages, representing another important class of complex networks.
It can also be studied using complex network theory. Over the
last decade, many papers on the interdisciplinary research between
software engineering and complex networks have been published.
It provides a different dimension to our understanding of software
and also is very useful for the design and development of software
systems. This paper will explore how to use the complex network
theory to analyze software structure, and briefly review the main
advances in corresponding aspects.", keywords = "Metrics, measurement, complex networks, software.", volume = "5", number = "12", pages = "1602-7", }
