graph arc (GraphArc)

Graphs are comprised of GraphNodes and GraphArcs. Every GraphArc links two GraphNodes.

Ontology

SUMO / GRAPH-THEORY

Superclass(es)

entity

abstract

graph element

graph arc

Subclass(es)

graph loop

Coordinate term(s)

graph node

Constrains relations

initial node fn terminal node fn arc weight links

Related WordNet synsets

See more related synsets on a separate page.

Axioms (5)

If graph is an instance of directed graph and arc is an instance of graph arc and arc is a part of graph, then there exist node1,node2 so that "the starting node of arc" is equal to node1 and "the terminal node of arc" is equal to node2.

(=>
      (and
            (instance ?GRAPH DirectedGraph)
            (instance ?ARC GraphArc)
            (graphPart ?ARC ?GRAPH))
      (exists
            (?NODE1 ?NODE2)
            (and
                  (equal
                        (InitialNodeFn ?ARC)
                        ?NODE1)
                  (equal
                        (TerminalNodeFn ?ARC)
                        ?NODE2))))

if graph is an instance of graph path and arc is an instance of graph arc and arc is a part of graph,
then if "the starting node of arc" is equal to node, then there doesn't exist other so that "the starting node of other" is equal to node and other is not equal to arc

(=>
      (and
            (instance ?GRAPH GraphPath)
            (instance ?ARC GraphArc)
            (graphPart ?ARC ?GRAPH))
      (=>
            (equal
                  (InitialNodeFn ?ARC)
                  ?NODE)
            (not
                  (exists
                        (?OTHER)
                        (and
                              (equal
                                    (InitialNodeFn ?OTHER)
                                    ?NODE)
                              (not
                                    (equal ?OTHER ?ARC)))))))

if graph is an instance of graph path and arc is an instance of graph arc and arc is a part of graph,
then if "the terminal node of arc" is equal to node, then there doesn't exist other so that "the terminal node of other" is equal to node and other is not equal to arc

(=>
      (and
            (instance ?GRAPH GraphPath)
            (instance ?ARC GraphArc)
            (graphPart ?ARC ?GRAPH))
      (=>
            (equal
                  (TerminalNodeFn ?ARC)
                  ?NODE)
            (not
                  (exists
                        (?OTHER)
                        (and
                              (equal
                                    (TerminalNodeFn ?OTHER)
                                    ?NODE)
                              (not
                                    (equal ?OTHER ?ARC)))))))

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

(partition GraphElement GraphNode GraphArc)

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)
            (links ?NODE1 ?NODE2 ?ARC)))