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Chapter 4. Measuring Evolving Software
links from a class (the out-degree). As discussed in Section 4.2.2, these
two measures are widely used in the literature as measures of structural
complexity [21, 54, 55, 77, 117, 165, 209, 223, 287, 294, 299] since
they naturally capture the number of classes a given class X depends
upon and the number of classes that depend on X.
For the purpose of measuring the dependencies we define two sets K
and N. The first set, K is a finite non-empty set of all classes in the
software system and includes the classes from the core software system,
as well as classes that provide services (to classes in the core) but are in
part of third-party libraries or the Java framework. The second set, N
contains classes that are part of the core software system such that N ⊂
K. The distinction between these two sets is illustrated in Figure 4.6.
The type dependency graph G T is an ordered pair < K, L >, where L
is a finite, possibly empty, set of directed links between classes, such
that, L ⊆ N × K. Our restriction of focusing on the core software system
(as discussed in Section 3.6.2) implies that we do not measure the
dependencies between classes in the external libraries and hence we
analyze only the set of links that are formed when classes within the
set N depend on classes in the set K. For example, the dependency
between classes A and B in Figure 4.6 is not part of the graph that we
construct. Additionally, classes A and B in Figure 4.6 are also not in
the set K.
4.5.5 Dependency Metric Extraction
Once the dependency graph has been constructed, we can analyze each
node n ∈ N in the graph as well as the set of directed links l ∈ L for
each node within the graph G T and measure the In-Degree Count l in (n),
as well as the Out-Degree Count l out (n) it. More precisely,
l in (n) = |{(n i , n) ∧ n i ∈ N ∧ n ̸= n i }| (4.5.1)
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