Difference between revisions of "Graph Metrics"
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Graph or structural metrics calculate the structure of ontologies. | Graph or structural metrics calculate the structure of ontologies. | ||
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| + | ==Absolute Root Cardinality== | ||
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| + | ==Absolute Leaf Cardinality== | ||
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| + | ==Absolute Sibling Cardinality== | ||
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| + | ==Depth== | ||
| + | Depth is a property of graphs which is related to cardinality of paths existing in the graph. The arcs which are considered are only isa arcs but this only applies to directed graphs. | ||
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| + | ===Absolute Depth=== | ||
| + | The value of the absolute depths is calculated as follows: | ||
| + | <math>m = \sum \j^P N\textsubscript{j \in P}</math> | ||
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| + | ===Average Depth=== | ||
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| + | 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. | ||
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| + | As reference values, there are also shown the '''maximal depth''' and '''absolute depth'''. | ||
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| + | ===Maximal Depth=== | ||
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| + | ==Absolute Breadth== | ||
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==Average Breadth== | ==Average Breadth== | ||
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As reference values, there are also shown the '''maximal breadth''' and '''absolute breadth'''. | As reference values, there are also shown the '''maximal breadth''' and '''absolute breadth'''. | ||
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| − | + | ==Maximal Breadth== | |
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==Density== | ==Density== | ||
Revision as of 10:45, 10 September 2016
Graph or structural metrics calculate the structure of ontologies.
Contents
Absolute Root Cardinality
Absolute Leaf Cardinality
Absolute Sibling Cardinality
Depth
Depth is a property of graphs which is related to cardinality of paths existing in the graph. The arcs which are considered are only isa arcs but this only applies to directed graphs.
Absolute Depth
The value of the absolute depths is calculated as follows: Failed to parse (unknown function "\j"): m = \sum \j^P N\textsubscript{j \in P}
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 absolute depth.
Maximal Depth
Absolute Breadth
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 values, there are also shown the maximal breadth and absolute breadth.
Maximal Breadth
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
- 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
