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ventions. This metric is the same as the previous one
but it applies on object properties instead of classes
and takes into account property names that begin
with a lower-case letter.
N3: Data-type properties with the same naming
conventions. Similarly, this metric is defined as in
the previous case but it applies on data-type
properties.
3.2 Concept Hierarchy/Taxonomy
Concept hierarchy expresses how well a specified
taxonomy is structured. The measurable criteria that
are used in order to assess this feature are associated
with the number of classes, average number of
parent and sibling nodes, as well as various metrics
about the characteristics of the tree taxonomy, such
as the tree depth, the internal and external paths, and
so forth. The total list of these criteria follows.
C1: Total Number of Classes. It is defined as the
number of classes in the ontology.
C2: Number of Primitive Classes. This metric
equals the number of classes in the ontology that
have necessary conditions. When necessary
conditions are defined for a class, any instance of
this class should necessarily fulfill these conditions.
However, if any instance fulfils these conditions,
this does not necessarily imply that it is also a
member of this class.
C3: Number of Defined Classes. It is equal to the
number of classes in the ontology that have at least
one set of necessary and sufficient conditions. When
necessary and sufficient conditions apply to a class,
any member, i.e., instance of this class should
necessarily fulfill these conditions, and vice versa, if
any instance fulfils these conditions then it is
certainly a member of this class.
C4: Average Number of Parents. This metric
expresses the average number of parent classes, or
“super-classes” based on each class in the taxonomy.
The greater the value of this metric is, the denser the
structure of the ontology becomes.
C5: Maximum Number of Parents. Similarly to the
previous metric, this one is equal to the maximum
number of super-classes that correspond to all
ontology classes. This is a structure-related metric
that expresses the maximum number of isa hierarchy
associations that are defined per class.
C6: Average Number of Siblings. This metric is the
average number of sibling classes, i.e., classes that
share the same parent of all ontology classes. This
metric expresses the average number of child nodes
per hierarchical level per parent class. As the value
of C6 increases, the ontology becomes denser, and
the number of child nodes increases per parent node.
C7: Maximum Number of Siblings. This metric
displays the maximum number of classes that share
the same parent node in the ontology. This is also a
metric of how dense an ontology is in terms of its
structure. A big value for C6 indicates a dense
ontology with a big number of child nodes per
parent node.
C8: Max Depth. Given an ontology tree, this
metric computes the maximum depth of the tree
structure, namely the number of nodes along the
longest path from the root node down to the farthest
leaf node. This metric indicates the number of
structure levels within the ontology. A big value for
C8 indicates that the taxonomy consists of many
hierarchy levels.
C9: Total Number of Nodes. It is the total number
of nodes in the ontology tree structure. This is a
metric about how dense is the ontology structure.
C10: Total Number of Roots. The total number of
nodes that belong to the topmost level in the
ontology tree hierarchy, i.e., the number of nodes
with no parents. This indicates the number of
independent classes that are defined within the same
taxonomy. It is a measure of ontology modularity.
C11: Total Number of Internal Nodes (Parents). It
is equal to the total number of nodes in the ontology
tree. Only nodes with child nodes are taken into
account. This metric expresses how dense is the
ontology structure.
C12: Total Number of Children. It is equal to the
total number of child nodes in the taxonomy, i.e.,
nodes with at least one parent node. This metric also
expresses the density of the tree structure.
C13: Total Number of External Nodes (Leaf). It is
defined as the total number of nodes in the ontology
tree structure that do not have any child nodes. Root
nodes are also taken into account for the calculation
of this metric. Again, this is a taxonomy-density
metric.
C14: Internal Path Length. It is equal to the sum
over all internal nodes of the paths from the root of
the taxonomy to each node, not including tree
leaves, i.e., nodes with no children. The depth for an
internal node is defined as the number of classes that
we come across when traversing the tree from the
root to the internal node.
C15: External Path Length. This metric is defined
as the sum over all external nodes, i.e., leaves, of the
lengths of the paths from the root to each node. Both
C14, C15 are metrics that express tree density.
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