Graph Metrics

Graph or structural metrics calculate the structure of ontologies.

Average Breadth

Breadth is a property related to the cardinality of levels (“generations”) in a graph, where the arcs considered here are only subClassOf arcs. This measure only applies to digraphs (directed graphs). The average breadth states at which degree the ontology has a horizontal modelling of hierarchies.

As reference value, there is also shown the maximal breadth.

Average Depth

Depth is a graph property related to the cardinality of paths in a graph, where the arcs considered here are only subClassOf arcs. This measure type only applies to digraphs (directed graphs). The average depth states at which degree the ontology has a vertical modelling of hierarchies.

As reference values, there are also shown the maximal depth and absolut depth.

Density

Density can be defined as the presence of clusters of classes with many non-taxonomical relations holding among them. For example, so-called core ontology patterns (for thematic roles in events, contracts, diagnoses, etc.) usually constitute dense areas in an ontology. To detect those areas, there are already several classifying techniques existing to be able to measure the absolute size and quantity.

Logical Adequacy

The logical adequacy of a graph is described by formal semantics where either directed or conceptual relations exist. Consistency ratio can be derived from it with 'nInc' of quantity cardinality from consistent classes of the graph 'g' and 'nG' of quantity cardinality from class knots of the graph 'g'.

Modularity

Modularity is related to the asserted modules of a graph, where the arcs considered here are either subClassOf or non-subClassOf arcs. In comparison to cohesion, the number of knots of connected components are put into proportion to the number of all graph elements. However, basically they describe equivalent metrics.

Fan-outness

Fan-outness is related to the “dispersion” of graph nodes, where the arcs considered here are subClassOf arcs.

Tangledness

Tangledness is related to the multihierarchical nodes of a graph, where the arcs considered here are again only subClassOf arcs. This measure only applies to digraphs. The tangledness of a class tree is subject of multiple hierarchy knots of a graph. It means, that this knot has more than one incoming edge.

Sources

1. Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann:
   Ontology evaluation and validation - An integrated formal model for the quality diagnostic task
   September 2005 , pp 11-16.
   http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf