graph node (GraphNode)

Graphs are comprised of GraphNodes and GraphArcs. Every GraphNode is linked by a GraphArc.

Ontology

SUMO / GRAPH-THEORY

Superclass(es)

entity

abstract

graph element

graph node

Coordinate term(s)

graph arc

Constrains relations

begin node fn end node fn graph path fn initial node fn maximal weighted path fn minimal weighted path fn terminal node fn links

Related WordNet synsets

See more related synsets on a separate page.

Axioms (3)

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

arc links node1 and node2
- path is a subgraph of graph
- path is an instance of graph path
- - "the beginning of path" is equal to node1 and "the end of path" is equal to node2
  - "the beginning of path" is equal to node2 and "the end of path" is equal to node1

(=>
      (and
            (instance ?GRAPH Graph)
            (instance ?NODE1 GraphNode)
            (instance ?NODE2 GraphNode)
            (graphPart ?NODE1 ?GRAPH)
            (graphPart ?NODE2 ?GRAPH)
            (not
                  (equal ?NODE1 ?NODE2)))
      (exists
            (?ARC ?PATH)
            (or
                  (links ?NODE1 ?NODE2 ?ARC)
                  (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)))))))

graph element is exhaustively partitioned into graph node,graph arc.

(partition GraphElement GraphNode GraphArc)

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)
            (links ?NODE ?OTHER ?ARC)))