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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University An Exploration of Power-law in Use-relation of Java Software Systems Makoto Ichii, Makoto Matsushita, Katsuro Inoue Osaka University 2008/3/26ASWEC 2008 1
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Software Component Graph A software system is composed of software components. Software component (component): building unit of a software system Complex use-relation is formed between components Software component graph (component graph) represents use-relation between components node: component / edge: use-relation Various researches utilize component graphs to analyze software systems It is important to know the nature of component graphs 2008/3/26ASWEC 2008 2
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Power-law distribution A graph is characterized by the degree distribution The graphs whose degree distribution follows the power-law distribution attracts attention in various research domains Link structure of WWW pages Hosts on the Internet Such graphs tend to have interesting characteristics Self similarity Fault tolerance 2008/3/26ASWEC 2008 3 Explore the component graphs to seek whether the degree distributions follow the power law p(x) = Cx - α
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Questions [1-2/4] Q. 1 Do the in- and out-degree distributions of a component graph of a software system follow the power law? 2008/3/26ASWEC 2008 4 Q. 2 Do the in- and out-degree distributions of a component graph of multiple software systems follow the power law? ? ?
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Questions [1-2/4] Q.](http://images.slideplayer.com./24/7053707/slides/slide_4.jpg "1 Do the in- and out-degree distributions of a component graph of a software system follow the power law. 2008/3/26ASWEC Q. 2 Do the in- and out-degree distributions of a component graph of multiple software systems follow the power law. .")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Questions [3-4/4] Q. 3 Do the in- and out-degree distributions of subgraph of a component graph follow the power law? 2008/3/26ASWEC 2008 5 Q. 4 What aspects of components affects the in- and out-degree distribution of component graphs? ?
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Questions [3-4/4] Q.](http://images.slideplayer.com./24/7053707/slides/slide_5.jpg "3 Do the in- and out-degree distributions of subgraph of a component graph follow the power law. 2008/3/26ASWEC Q. 4 What aspects of components affects the in- and out-degree distribution of component graphs. .")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Definitions [1/2] Component: Java class (including interface) Use-relation: Any of the following six relation types acquired by static analysis of the component source files. A class or an interface extends another class or interface respectively. A class implements an interface. A class or an interface declares a variable of a class or an interface. A class instantiates a class object. A class calls a method of a class or an interface. A class or an interface references to a field variable of a class or an interface. 2008/3/26ASWEC 2008 6
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Definitions [1/2] Component: Java class (including interface) Use-relation: Any of the following six relation types acquired by static analysis of the component source files.](http://images.slideplayer.com./24/7053707/slides/slide_6.jpg " A class or an interface extends another class or interface respectively. A class implements an interface. A class or an interface declares a variable of a class or an interface. A class instantiates a class object. A class calls a method of a class or an interface. A class or an interface references to a field variable of a class or an interface. 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Definitions [2/2] Component graph: Directed simple graph node: component edge: use-relation between components In-(Out-)degree: The number of incoming (outgoing) edges to a node 2008/3/26ASWEC 2008 7 class B { … A.exec(); … } class A { void exec() { … } A B class C { … A a = new A(); … } C in-degree: 2 out-degree: 0 in-degree: 0 out-degree: 1 in-degree: 0 out-degree: 1
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Definitions [2/2] Component graph: Directed simple graph node: component edge: use-relation between components In-(Out-)degree: The number of incoming (outgoing) edges to a node 2008/3/26ASWEC class B { … A.exec(); … } class A { void exec() { … } A B class C { … A a = new A(); … } C in-degree: 2 out-degree: 0 in-degree: 0 out-degree: 1 in-degree: 0 out-degree: 1](http://images.slideplayer.com./24/7053707/slides/slide_7.jpg "Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Definitions [2/2] Component graph: Directed simple graph node: component edge: use-relation between components In-(Out-)degree: The number of incoming (outgoing) edges to a node 2008/3/26ASWEC class B { … A.exec(); … } class A { void exec() { … } A B class C { … A a = new A(); … } C in-degree: 2 out-degree: 0 in-degree: 0 out-degree: 1 in-degree: 0 out-degree: 1")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Observing the power-law Plot cumulative frequency on log- log axis The data forms a straight line if the distribution is the power law 2008/3/26ASWEC 2008 8 gradient : -α gradient : -(α-1) p(x) = Cx - α in-(or out-)degree M. E. J. Newman, "Power laws, Pareto distributions and Zipf's law", Contemporary Physics 46, 323-351 (2005)
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Values shown in the experiments α: exponent Derive from the gradient of the regression line R *2 : the determination coefficient adjusted for the degree of freedom Fitness of a regression model for data [0..1] Large value means good fitness 2008/3/26ASWEC 2008 9 gradient : -(α-1) p(x) = Cx - α in-(or out-)degree
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Values shown in the experiments α: exponent Derive from the gradient of the regression line R *2 : the determination coefficient adjusted for the degree of freedom Fitness of a regression model for data [0..1] Large value means good fitness 2008/3/26ASWEC gradient : -(α-1) p(x) = Cx - α in-(or out-)degree](http://images.slideplayer.com./24/7053707/slides/slide_9.jpg "Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Values shown in the experiments α: exponent Derive from the gradient of the regression line R *2 : the determination coefficient adjusted for the degree of freedom Fitness of a regression model for data [0..1] Large value means good fitness 2008/3/26ASWEC gradient : -(α-1) p(x) = Cx - α in-(or out-)degree")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Experiment 1 Setup component sets Each set contains a single software system Analyze component sets to create component graphs. Plot cumulative frequency of the degrees on log-log axis. 2008/3/26ASWEC 2008 10 Q. 1 Do the in- and out-degree distributions of a component graph of a software system follow the power law? Description# of components JDKJava 2 SE Software Development Kit 1.411,556 ECLIPSEEclipse 3.0.113,941
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 1 / JDK 2008/3/26ASWEC 2008 11 αR *2 in-degree 2.1 ±8.6×10 -3 0.99 out-degree 3.1 ±8.2×10 -2 0.88 ►The in-degree follows the power law ►The out-degree does not follow the power law # of Nodes11,556 # of Edges107,198
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 1 / ECLIPSE 2008/3/26ASWEC 2008 12 ►The similar characteristics with JDK The in-degree follows the power law The out-degree does not follow the power law αR *2 in-degree 2.2 ±1.6×10 -2 0.96 out-degree 3.0 ±7.7×10 -2 0.86 # of Nodes13,941 # of Edges140,678
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Experiment 2 Setup component sets Each set contains multiple software systems Use-relation across the systems exists Analyze component sets to create component graphs. Plot cumulative frequency of the degrees on log-log axis. 2008/3/26ASWEC 2008 13 Q. 2 Do the in- and out-degree distributions of a component graph for multiple software systems follow the power law? Description# of components ASFVarious projects checked out from the repository of Apache Software Foundation 59,486 SPARS_DBThe components stored in the database of demo.spars.info (includes ASF, JDK) 180,637
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 2 / ASF 2008/3/26ASWEC 2008 14 ►The similar characteristics with Exp. 1 The in-degree follows the power law The out-degree does not follow the power law αR *2 in-degree 2.4 ±1.1×10 -2 0.98 out-degree 3.4±6.4×10 -2 0.94 # of Nodes59,486 # of Edges303,755
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 2 / SPARS_DB 2008/3/26ASWEC 2008 15 αR *2 in-degree 2.0 ±1.5×10 -3 1.00 out-degree 3.7 ±7.0×10 -2 0.90 # of Nodes180,637 # of Edges1,808,982 ►The similar characteristics with Exp. 1 The in-degree follows the power law The out degree does not follow the power-law completely ►In-degree distribution fits to the power-law straight line almost ideally.
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Experiment 3 Construct subsets of SPARS_DB Keyword: The components that contain a specified keyword in the source code The keywords are randomly selected so that the number of resulting components is about 1,000/10,000 Random: 1,000/10,000 random components Analyze component sets to create component graphs. Plot cumulative frequency of the degrees on log-log axis. 2008/3/26ASWEC 2008 16 Q. 3 Do the in- and out-degree distributions of subgraph of a component graph for software systems follow the power law? Description# of components KWD1KThe components that contain “labels”1,002 KWD10KThe components that contain “getstring”8,938 RND1KRandomly-selected 1,000 components1,000 RND10KRandomly-selected 10,000 components10,000
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 3 / KWD1K 2008/3/26ASWEC 2008 17 αR *2 in-degree 2.2 ±3.3×10 -2 0.98 out-degree 3.7 ±2.0×10 -1 0.93 # of Nodes1,002 # of Edges1,564 ►The similar characteristics with SPARS_DB The in-degree follows the power law The out-degree does not follow the power law
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 3 / KWD10K 2008/3/26ASWEC 2008 18 αR *2 in-degree 2.1 ±9.3×10 -3 0.99 out-degree 3.4 ±2.7×10 -1 0.93 # of Nodes8,938 # of Edges24,317 ►The similar characteristics with SPARS_DB The in-degree follows the power law The out-degree does not follow the power law
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 3 / RND1K 2008/3/26ASWEC 2008 19 αR *2 in-degree 2.3 ±1.8×10 -1 0.93 out-degree N/A # of Nodes1,000 # of Edges52 ►The original characteristics is almost lost
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 3 / RND10K 2008/3/26ASWEC 2008 20 αR *2 in-degree 1.9 ±2.1×10 -2 0.98 out-degree 4.3 ±3.3×10 -1 0.91 # of Nodes10,000 # of Edges6,184 ►The similar characteristics with SPARS_DB, however # of edges is small
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Experiment 4 List top-ten components in the in- and out-degree Calculate correlation between degrees and metric values. Spearman's rank correlation coefficient Target: SPARS_DB 2008/3/26ASWEC 2008 21 Q. 4 What aspects of components affects the in- and out-degree distribution of component graphs? MetricDescription LOCNon-comment source lines of code WMC1A variation of weighted methods per class (WMC) Weight of a method: constant value (1) WMC2A variation of WMC Weight of a method: Cyclomatic complexity LCOMA variation of lack of cohesion of methods: LCOM5
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 4 / In-degree Top-ten components The components that have fundamental/general role Correlation with metrics In-degree have low correlation with the metrics The in-degree relates to the role 2008/3/26ASWEC 2008 22 NameLOC In- degre e Out- degre e 1java.lang.String675116,23921 2java.lang.Object3598,2614 3java.lang.Class60529,68241 4java.lang.Exception1521,0462 5java.lang.Throwable13619,51912 6java.lang.System17019,17527 7java.util.Iterator515,5221 8java.util.List2714,4624 9java.util.ArrayList20013,65619 10java.lang.Integer28512,7369 Out- degree LOCWMC1 LCOM In- degree 0.000.070.240.080.12
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Result of experiment 4 / Out-degree Top-ten components Simply large/complex classes Correlation with metrics High correlation with LOC and WMC The out-degree relates to the size/complexity of a component 2008/3/26ASWEC 2008 23 In- degree LOCWMC1 LCOM Out- degree 0.000.820.640.750.39 NameLOC In- degre e Out- degre e 1org.apache...FunctionEval3641354 2org.jgraph.GPGraphpad2,196130255 3com.jgraph.GPGraphpad2,200131253 4org.jgraph.GPGraphpad542209252 5 org.eclipse... ASTConverter4,5203223 6org.eclipse...JavaEditor1,368115220 7 net.sourceforge... GanttProject3,05598216 8 it.businesslogic... MainFrame7,17746204 9 org... InstConstraintVisitor1,6263197 10 org... ASTInstructionCompiler2,4491189
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [1/4] Q. 1 Do the in- and out-degree distributions of a component graph of a software system follow the power law? The in-degree follows the power law The out-degree does not follow the power law Mixture of the power-law distribution and the lognormal distribution 2008/3/26ASWEC 2008 24
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [1/4] Q.](http://images.slideplayer.com./24/7053707/slides/slide_24.jpg "1 Do the in- and out-degree distributions of a component graph of a software system follow the power law. The in-degree follows the power law The out-degree does not follow the power law Mixture of the power-law distribution and the lognormal distribution 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [2/4] Q. 2 Do the in- and out-degree distributions of a component graph for multiple software systems follow the power law? The in-degree follows the power law The out-degree does not follow the power law The similar results with that of single software systems 2008/3/26ASWEC 2008 25
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [2/4] Q.](http://images.slideplayer.com./24/7053707/slides/slide_25.jpg "2 Do the in- and out-degree distributions of a component graph for multiple software systems follow the power law. The in-degree follows the power law The out-degree does not follow the power law The similar results with that of single software systems 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [3/4] Q. 3 Do the in- and out-degree distributions of subgraph of a component graph for software systems follow the power law? Depends on how the subgraph is created. Keyword-based subgraph has similar characteristics with the superset Related components likely share words Random-selection-based subgraph with small number of nodes has different characteristics Few edges exist. 2008/3/26ASWEC 2008 26
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [3/4] Q.](http://images.slideplayer.com./24/7053707/slides/slide_26.jpg "3 Do the in- and out-degree distributions of subgraph of a component graph for software systems follow the power law. Depends on how the subgraph is created. Keyword-based subgraph has similar characteristics with the superset Related components likely share words Random-selection-based subgraph with small number of nodes has different characteristics Few edges exist. 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [4/4] Q. 4 What aspects of components affects the in- and out-degree distribution of component graphs? In-degree relates to the roles of components Most of the components are used at the specific part Components with fundamental/general role are used from everywhere The more the size of component set grows, the more the value of in-degree becomes large. Out-degree relates to size/complexity of components Many components have reasonable size/complexity Some components may have relatively large size/complexity Extremely large components are unreasonable 2008/3/26ASWEC 2008 27
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Answers: summary of experiments [4/4] Q.](http://images.slideplayer.com./24/7053707/slides/slide_27.jpg "4 What aspects of components affects the in- and out-degree distribution of component graphs. In-degree relates to the roles of components Most of the components are used at the specific part Components with fundamental/general role are used from everywhere The more the size of component set grows, the more the value of in-degree becomes large. Out-degree relates to size/complexity of components Many components have reasonable size/complexity Some components may have relatively large size/complexity Extremely large components are unreasonable 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Summary Component graphs are investigated to seek whether the in- and out-degree distribution follows the power-law As the results, following characteristics are revealed. The in-degree distribution follows the power-law The in-degree of a component relates to the role of the component The out-degree distribution does not follows the power-law The out-degree of a component relates to the size/complexity of the component Some sort of subgraph of a component graph have the same characteristics of degree distribution with the graph. Future works Explore the other types of component graph 2008/3/26ASWEC 2008 28
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University 2008/3/26ASWEC 2008 29
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University + 2008/3/26ASWEC 2008 30
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University SPARS_DB Repositories :pserver:anoncvs@cvs.apache.org:/home/cvspublic :pserver:anoncvs@cvs.netbeans.org:/cvs :pserver:anonymous@dev.eclipse.org:/home/eclipse :pserver:anonymous@cvs.sourceforge.net:/cvsroot/azureus :pserver:anonymous@cvs.sourceforge.net:/cvsroot/borg-calendar :pserver:anonymous@cvs.sourceforge.net:/cvsroot/care2002 :pserver:anonymous@cvs.sourceforge.net:/cvsroot/celldb :pserver:anonymous@cvs.sourceforge.net:/cvsroot/cycleatlas :pserver:anonymous@cvs.sourceforge.net:/cvsroot/fipa-os :pserver:anonymous@cvs.sourceforge.net:/cvsroot/freecbr :pserver:anonymous@cvs.sourceforge.net:/cvsroot/freemind :pserver:anonymous@cvs.sourceforge.net:/cvsroot/gals :pserver:anonymous@cvs.sourceforge.net:/cvsroot/ganttproject :pserver:anonymous@cvs.sourceforge.net:/cvsroot/gnucashtoqif :pserver:anonymous@cvs.sourceforge.net:/cvsroot/gnujpdf :pserver:anonymous@cvs.sourceforge.net:/cvsroot/goalseeker :pserver:anonymous@cvs.sourceforge.net:/cvsroot/hambo :pserver:anonymous@cvs.sourceforge.net:/cvsroot/hipergate :pserver:anonymous@cvs.sourceforge.net:/cvsroot/iharder :pserver:anonymous@cvs.sourceforge.net:/cvsroot/ij-plugins :pserver:anonymous@cvs.sourceforge.net:/cvsroot/ipodder :pserver:anonymous@cvs.sourceforge.net:/cvsroot/irate :pserver:anonymous@cvs.sourceforge.net:/cvsroot/ireport :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jabref :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jajuk :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jatlas :pserver:anonymous@cvs.sourceforge.net:/cvsroot/javahmo :pserver:anonymous@cvs.sourceforge.net:/cvsroot/javanmea :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jboss :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jdbcexplorer :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jdrawing :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jedit :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jgnash :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jgraph :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jkaiui :pserver:anonymous@cvs.sourceforge.net:/cvsroot/jose-chess :pserver:anonymous@cvs.sourceforge.net:/cvsroot/junitee :pserver:anonymous@cvs.sourceforge.net:/cvsroot/kt-dms :pserver:anonymous@cvs.sourceforge.net:/cvsroot/luntbuild :pserver:anonymous@cvs.sourceforge.net:/cvsroot/nwn-j3d :pserver:anonymous@cvs.sourceforge.net:/cvsroot/openantivirus :pserver:anonymous@cvs.sourceforge.net:/cvsroot/oreports :pserver:anonymous@cvs.sourceforge.net:/cvsroot/osexpress :pserver:anonymous@cvs.sourceforge.net:/cvsroot/proteinmusic :pserver:anonymous@cvs.sourceforge.net:/cvsroot/safepeer :pserver:anonymous@cvs.sourceforge.net:/cvsroot/sax :pserver:anonymous@cvs.sourceforge.net:/cvsroot/schemamap :pserver:anonymous@cvs.sourceforge.net:/cvsroot/sheltermanager :pserver:anonymous@cvs.sourceforge.net:/cvsroot/simpleprofiler :pserver:anonymous@cvs.sourceforge.net:/cvsroot/simplethread :pserver:anonymous@cvs.sourceforge.net:/cvsroot/sshtools :pserver:anonymous@cvs.sourceforge.net:/cvsroot/timcam :pserver:anonymous@cvs.sourceforge.net:/cvsroot/ultravnc :pserver:anonymous@cvs.sourceforge.net:/cvsroot/utbot :pserver:anonymous@cvs.sourceforge.net:/cvsroot/vnc-tight :pserver:anonymous@cvs.sourceforge.net:/cvsroot/web-portal :pserver:anonymous@cvs.sourceforge.net:/cvsroot/xmlhelper :pserver:anonymous@cvs.sourceforge.net:/cvsroot/xweb 2008/3/26ASWEC 2008 31 57 repositories / 750 modules
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University ASF Modules (projects) 107 modules ant ant-antidote avalon avalon-components avalon-excalibur avalon-logkit avalon- phoenix avalon-sandbox cocoon-1 cocoon-2-historical cocoon-2.0 cocoon-2.1 cocoon-2.2 cocoon-lenya db-commons db-commons-sandbox db-ojb db-torque jakarta-alexandria jakarta-bcel jakarta-bsf jakarta-cactus jakarta-commons jakarta- commons-sandbox jakarta-ecs jakarta-ecs2 jakarta-hivemind jakarta-jetspeed jakarta-jetspeed-2 jakarta-jmeter jakarta-log4j jakarta-log4j-sandbox jakarta-lucene jakarta-lucene-sandbox jakarta-ojb jakarta-oro jakarta-pluto jakarta-poi jakarta- regexp jakarta-servletapi jakarta-servletapi-4 jakarta-servletapi-5 jakarta-slide jakarta-struts jakarta-taglibs jakarta-taglibs-sandbox jakarta-tapestry jakarta-tomcat jakarta-tomcat-4.0 jakarta-tomcat-5 jakarta-tomcat-catalina jakarta-tomcat- connectors jakarta-tomcat-jasper jakarta-tomcat-service jakarta-tools jakarta- turbine-2 jakarta-turbine-3 jakarta-turbine-flux jakarta-turbine-fulcrum jakarta- turbine-jcs jakarta-turbine-jyve jakarta-turbine-orgami jakarta-turbine-stratum jakarta-turbine-tdk jakarta-turbine-torque jakarta-velocity jakarta-velocity-dvsl jakarta-velocity-tools jakarta-watchdog jakarta-watchdog-4.0 james-server logging- log4j logging-log4j-attic logging-log4j-sandbox maven maven-components maven- jelly-tags maven-plugins maven-plugins-sandbox maven-scm maven-wagon ws- admin ws-axis ws-fx ws-jaxme ws-juddi ws-soap ws-wsif ws-wsil ws-wsrp4j ws- xmlrpc xml-admin xml-axkit xml-batik xml-cocoon2 xml-commons xml-contrib xml- crimson xml-fop xml-forrest xml-security xml-stylebook xml-xalan xml-xang xml- xerces xml-xindice xml-xmlbeans 2008/3/26ASWEC 2008 32
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.3 / More Results for Keyword-based subset [1/2] Histogram of α / R* 2 of in-degree The keywords submitted to demo.spars.info as search queries 2008/3/26ASWEC 2008 33
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.3 / More Results for Keyword-based subset [1/2] Histogram of α / R* 2 of in-degree The keywords submitted to demo.spars.info as search queries 2008/3/26ASWEC](http://images.slideplayer.com./24/7053707/slides/slide_33.jpg "Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.3 / More Results for Keyword-based subset [1/2] Histogram of α / R* 2 of in-degree The keywords submitted to demo.spars.info as search queries 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.3 / More Results for Keyword-based subset [2/2] X-axis: the number of components in subset 2008/3/26ASWEC 2008 34
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.3 / More Results for Keyword-based subset [2/2] X-axis: the number of components in subset 2008/3/26ASWEC](http://images.slideplayer.com./24/7053707/slides/slide_34.jpg "Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.3 / More Results for Keyword-based subset [2/2] X-axis: the number of components in subset 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.4 / Cross-correlation 2008/3/26ASWEC 2008 35
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.4 / Scatter plot [1/2] 2008/3/26ASWEC 2008 36
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.4 / Scatter plot [1/2] 2008/3/26ASWEC](http://images.slideplayer.com./24/7053707/slides/slide_36.jpg "Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.4 / Scatter plot [1/2] 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.4 / Scatter plot [2/2] 2008/3/26ASWEC 2008 37
![Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.4 / Scatter plot [2/2] 2008/3/26ASWEC](http://images.slideplayer.com./24/7053707/slides/slide_37.jpg "Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Supplements for Exp.4 / Scatter plot [2/2] 2008/3/26ASWEC")
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Discussion Generative models of a power-law graph If a node is added to a graph, the nodes with large degree tend to get the edge to the new node. “rich get richer” Meanings for component graphs If a new component is added to (developed for) a software system, the new component uses the component that is already used by many components The members of frequently-used components hardly change even if the software development proceeds If the member changes, it means that the fundamental structure (design, architecture) of the software is changed 2008/3/26ASWEC 2008 38
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Clustering Coefficient (of a node) The connectivity between the nodes connected to the target node C i =n/ k i C 2 n : # edges between the nodes that connects to node i k i : the degree of node i 2008/3/26ASWEC 2008 39 3/ 4 C 2 = 0.5
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Clustering Coefficient and Hierarchical Organization C(k): average clustering coefficient of nodes whose degree= k A graph has hierarchical organization if C(k) ～ k -1 2008/3/26ASWEC 2008 40 E. Ravasz, A.L. Barabasi, "Hierarchical organization in complex networks",Physical Review E, vol 67, 261121, 2003.
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Software Engineering Laboratory, Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Clustering Coefficient and Hierarchical Organization / Result 2008/3/26ASWEC 2008 41 JDK SPARS_DB KWD1K(“labels”) C(k) ～ k 0.80 C(k) ～ k 0.93 C(k) ～ k 0.96
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