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a TernaryPredicate that specifies the GraphArc connecting two GraphNodes.

## Ontology

SUMO / GRAPH-THEORY

## Class(es)

 class

inheritable relation

ternary predicate

## Coordinate term(s)

altitude  between  capability  conditional probability  confers obligation  confers right  connects  depth  distance  domain  domain subclass  has purpose for agent  occupies position  orientation  prefers  related external concept  represents for agent  represents in language  temporally between  temporally between or equal

## Type restrictions

links(graph node, graph node, graph arc)

## Axioms (7)

If graph is an instance of graph and node1 is an instance of graph node and node2 is an instance of graph node and node1 is a part of graph and node2 is a part of graph and node1 is not equal to node2, then there exist arc,path so that
```(=>
(and
(instance ?GRAPH Graph)
(instance ?NODE1 GraphNode)
(instance ?NODE2 GraphNode)
(graphPart ?NODE1 ?GRAPH)
(graphPart ?NODE2 ?GRAPH)
(not
(equal ?NODE1 ?NODE2)))
(exists
(?ARC ?PATH)
(or
(and
(subGraph ?PATH ?GRAPH)
(instance ?PATH GraphPath)
(or
(and
(equal
(BeginNodeFn ?PATH)
?NODE1)
(equal
(EndNodeFn ?PATH)
?NODE2))
(and
(equal
(BeginNodeFn ?PATH)
?NODE2)
(equal
(EndNodeFn ?PATH)
?NODE1)))))))```

If graph is an instance of graph, then there exist node1,node2,node3,arc1,arc2 so that node1 is a part of graph and node2 is a part of graph and node3 is a part of graph and arc1 is a part of graph and arc2 is a part of graph and node2 links arc1 and node1 and node3 links arc2 and node2 and node1 is not equal to node2 and node2 is not equal to node3 and node1 is not equal to node3 and arc1 is not equal to arc2.
```(=>
(instance ?GRAPH Graph)
(exists
(?NODE1 ?NODE2 ?NODE3 ?ARC1 ?ARC2)
(and
(graphPart ?NODE1 ?GRAPH)
(graphPart ?NODE2 ?GRAPH)
(graphPart ?NODE3 ?GRAPH)
(graphPart ?ARC1 ?GRAPH)
(graphPart ?ARC2 ?GRAPH)
(not
(equal ?NODE1 ?NODE2))
(not
(equal ?NODE2 ?NODE3))
(not
(equal ?NODE1 ?NODE3))
(not
(equal ?ARC1 ?ARC2)))))```

graph is an instance of multi graph if and only if there exist arc1,arc2,node1,node2 so that arc1 is a part of graph and arc2 is a part of graph and node1 is a part of graph and node2 is a part of graph and arc1 links node1 and node2 and arc2 links node1 and node2 and arc1 is not equal to arc2.
```(<=>
(instance ?GRAPH MultiGraph)
(exists
(?ARC1 ?ARC2 ?NODE1 ?NODE2)
(and
(graphPart ?ARC1 ?GRAPH)
(graphPart ?ARC2 ?GRAPH)
(graphPart ?NODE1 ?GRAPH)
(graphPart ?NODE2 ?GRAPH)
(not
(equal ?ARC1 ?ARC2)))))```

If node is an instance of graph node, then there exist other,arc so that arc links node and other.
```(=>
(instance ?NODE GraphNode)
(exists
(?OTHER ?ARC)

If arc is an instance of graph arc, then there exist node1,node2 so that arc links node1 and node2.
```(=>
(instance ?ARC GraphArc)
(exists
(?NODE1 ?NODE2)
```(<=>
```(=>