Characteristics of Class Collaboration Networks in Large Java Software Projects

Characteristics of Class Collaboration Networks in Large

Java Software Projects

Miloš Savić, Mirjana Ivanović, Miloš Radovanović

Department of Mathematics and InformaticsFaculty 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

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

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

Class Collaboration Networks- Example -

Content


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

B C

DE

Characteristics of complex networks - Small world property -

• Relatively short path between any two nodes

• L ~ ln(N) – small world phenomena

• L ~ lnln(N) - ultra small world phenomena

1

2

3

4

5

6

7

nlL

nll

n

ii

n

ijj

iji

/

)1/(

1

1

l15=2 [125]

l17=4 [1346 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

3

1

23*4

2

2

)1(

ii

ii kk

EC

Content


Mathematical models of complex networks

• Erdőos-Rényi /ER/ modelrandom networks

• Barabási-Albert /BA/ modelscale-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

jj

ii k

kk

)( the probability that the new node connects

to a node with k links is proportional to k

kkP ~)(

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

Mathematical models of complex networks- BA model -

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 B2. Class A gives an incoming link to class B if B is in the same package as A, and A references B3. 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


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

Class collaboration network

γ[in] R2 γ[out] R2

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- In/Out Degree distributions -

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.Project

org.apache.tools.ant.BuildException

org.apache.tools.ant.Task

1.5.4: 536 nodes, 2241 links1.6.0: 114 new nodes, 525 new links

(336, 63)

(220, 43)

(124, 22)

Experiments and results- Ant CCN Evolution -

1.6.5: 690 nodes, 3000 links1.7.0: 132 new nodes, 44 deleted nodes, 634 new links

org.apache.tools.ant.Project

org.apache.tools.ant.BuildException(417, 69)

(269, 44)

Content


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

Characteristics of Class Collaboration Networks in Large

Java Software Projects

Miloš Savić, Mirjana Ivanović, Miloš Radovanović

Department of Mathematics and InformaticsFaculty of Science

University of Novi Sad

Characteristics of Class Collaboration Networks in Large Java Software Projects

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