Characteristics of Class Collaboration Networks in Large Java Software Projects

1
Characteristics of Class Collaboration Networks
in Large Java Software Projects

• Miloš Savic, Mirjana Ivanovic, Miloš Radovanovic
• Department of Mathematics and InformaticsFaculty
  of ScienceUniversity of Novi Sad

2
Content

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

3
Content

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

4
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

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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()

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Content

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

7
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
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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

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1
4
7
5
2
l152 1?2?5 l174 1?3?4?6 ? 7
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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
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Content

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

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Mathematical models of complex networks

• Erdoos-Rényi /ER/ modelrandom networks
• Barabási-Albert /BA/ modelscale-free networks

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Mathematical models of complex networks- ER
model -
Alg Generate ER networkInput p connection
probability 0..1n number of nodesOutput
ER networkfor (i 1 i lt n i) for (j
0 j lt i j) if (p lt rand(0, 1))
Connect(i, j)
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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
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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
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Content

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

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Network Extraction

• Class diagrams/JavaDoc/Source code
• YACCNE Jung, JavaCC
• Node connecting rules1. 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 its full package
  path 4. References that come outside the
  software system are excluded

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Content

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

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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?

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Experiments and results - JDK -
Our work (Valverde and Solé, 2003)
?in 2.17493 2.18
?out 3.63214 3.39
Small-world coefficient 4.391 5.40
Clustering coefficient 0.453 0.225
Extraction method Source code Class diagrams
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Experiments and results - In/Out Degree
distributions -
Class collaboration network ?in R2 ?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
?in lt ?out (except JavaCC) Same result
for variuos CCNs Myers(2003), Valverde and Solé,
2003
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Experiments and results - Small world and
clustering coefficient -
nodes links l c crand
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
lTomcat lnln(NTomcat) lJavaCC
lnln(NJavaCC) c gtgt crand
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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
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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
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Content

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

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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 Ants class
  collaboration network evolution

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Characteristics of Class Collaboration Networks
in Large Java Software Projects

• Miloš Savic, Mirjana Ivanovic, Miloš Radovanovic
• Department of Mathematics and InformaticsFaculty
  of ScienceUniversity of Novi Sad