Miloš Savić, Mirjana Ivanović, Miloš Radovanović Characteristics of Class Collaboration Networks in Large Java Software Projects Miloš Savić, Mirjana Ivanović, Miloš Radovanović Department of Mathematics and Informatics Faculty of Science University of Novi Sad

Content Class collaboration networks Characteristics of complex networks Mathematical models of complex networks Network extraction Experiments and results Conclusion

Content Class collaboration networks Characteristics of complex networks Mathematical models of complex networks Network extraction Experiments and results Conclusion

Class Collaboration Networks - Definition - Software – complex, modular, interacting system Java Class Collaboration Networks: * nodes – classes/interfaces * links – interactions among classes/interfaces Interaction ↔ Reference * Class A instantiates and/or uses objects of class B * Class A extends class B * Class A implements interface B

Class collaboration networks Class Collaboration Networks - Example - interface A { … } class B implements A { … } class C { … public void methodC(B b) { b.someMethod(); } class D extends C implements A { public B makeB() { return new B(); } C D A B

Content Class collaboration networks Characteristics of complex networks Mathematical models of complex networks Network extraction Experiments and results Conclusion

Characteristics of complex networks - Degree distribution - Node degree: number of links for the node Distribution function P(k) * probability that a randomly selected node has exactly k links Directed graph: incoming and outgoing degree distributions A E D B C

Characteristics of complex networks - Small world property - 3 Relatively short path between any two nodes L ~ ln(N) – small world phenomena L ~ lnln(N) - ultra small world phenomena 6 1 4 7 5 2 l15=2 [125] l17=4 [1346  7]

Characteristics of complex networks - Clustering coefficient - Tendency to cluster Node i - ki links to ki nodes (neighbours) - Ei – number of links between neighbours Neighbours with node i forms complete subgraph  Ci = 1 i

Content Class collaboration networks Characteristics of complex networks Mathematical models of complex networks Network extraction Experiments and results Conclusion

Mathematical models of complex networks Erdőos-Rényi /ER/ model random networks Barabási-Albert /BA/ model scale-free networks

Mathematical models of complex networks - ER model - Alg: Generate ER network Input: p – connection probability [0..1] n – number of nodes Output: ER network for (i = 1; i < n; i++) for (j = 0; j < i; j++) if (p <= rand(0, 1)) Connect(i, j);

Mathematical models of complex networks - BA model - Start with small random graph Growth * in each iteration add new node with m links Preferential attachment * new node prefers to link to highly connected nodes the probability that the new node connects to a node with k links is proportional to k

Mathematical models of complex networks - BA model - 1. The most of real/engineered networks are scale-free and can be modeled by BA model and its modifications 2. Both models can produce small world property 3. Clustering coefficient of scale-free network is much larger than in a comparable random network

Content Class collaboration network Characteristics of complex networks Mathematical models of complex networks Network extraction Experiments and results Conclusion

Network Extraction Class diagrams/JavaDoc/Source code YACCNE * Jung, JavaCC Node connecting rules 1. Class A gives an incoming link to class B if A imports B 2. Class A gives an incoming link to class B if B is in the same package as A, and A references B 3. Class A gives an incoming link to class B if A references B through it’s full package path 4. References that come outside the software system are excluded

Content Class collaboration network Characteristics of complex networks Mathematical models of complex networks Network extraction Experiments and results Conclusion

Experiments and results - Experiments - JDK, Tomcat, Ant, Lucene, JavaCC - cumulative incoming/outgoing link degree distributions - small-world coefficient - clustering coefficient Ten successive versions of Ant (from 1.5.2 to 1.7.0) - compared - can preferential attachment rule model Ant evolution?

Experiments and results - JDK - Our work (Valverde and Solé, 2003) γ[in] 2.17493 2.18 γ[out] 3.63214 3.39 Small-world coefficient 4.391 5.40 Clustering coefficient 0.453 0.225 Extraction method Source code Class diagrams

Experiments and results - In/Out Degree distributions - Class collaboration network γ[in] R2 γ[out] JDK 2.17493 0.9541 3.63214 0.9667 Ant 2.05001 0.9927 3.93654 0.9281 Tomcat 2.35234 0.9294 3.5026 0.9499 Lucene 1.98075 0.9050 4.29761 0.9028 JavaCC 2.26362 0.8946 2.20816 0.9656 γ[in] < γ[out] (except JavaCC) Same result for variuos CCNs: Myers(2003), Valverde and Solé, 2003

Experiments and results - Small world and clustering coefficient - #nodes #links l c c[rand] JDK 1878 12806 4.391 0.453 0.0036 Ant 778 3634 4.131 0.505 0.006 Tomcat 1046 4646 1.909 0.464 0.0042 Lucene 354 2221 2.2778 0.386 0.0177 JavaCC 79 274 1.22 0.437 0.0439 l[Tomcat] ~ lnln(N[Tomcat]) l[JavaCC] ~lnln(N[JavaCC]) c >> c[rand]

Experiments and results - Ant CCN Evolution - org.apache.tools.ant.BuildException (336, 63) org.apache.tools.ant.Project (220, 43) org.apache.tools.ant.Task (124, 22) 1.5.4: 536 nodes, 2241 links 1.6.0: 114 new nodes, 525 new links

Experiments and results - Ant CCN Evolution - org.apache.tools.ant.BuildException (417, 69) org.apache.tools.ant.Project (269, 44) 1.6.5: 690 nodes, 3000 links 1.7.0: 132 new nodes, 44 deleted nodes, 634 new links

Content Class collaboration network Characteristics of complex networks Mathematical models of complex networks Network extraction Experiments and results Conclusion

Conclusion Analyzed networks exhibit scale-free (or nearly scale-free) and small-world properties. The preferential attachment concept introduced in the BA model can explain Ant’s class collaboration network evolution

Miloš Savić, Mirjana Ivanović, Miloš Radovanović Characteristics of Class Collaboration Networks in Large Java Software Projects Miloš Savić, Mirjana Ivanović, Miloš Radovanović Department of Mathematics and Informatics Faculty of Science University of Novi Sad