Select language: english | cesky | deutsch | italiano | simplified chinese | traditional chinese | hindi Concept: English word: Home

# initial node fn (InitialNodeFn)

A UnaryFunction that maps a GraphArc to the initial node of the GraphArc. Note that this is a partial function. In particular, the function is undefined for GraphArcs that are not part of a DirectedGraph.

## Ontology

SUMO / GRAPH-THEORY

## Class(es)

 class

inheritable relation

unary function

initial node fn

## Coordinate term(s)

absolute value fn  abstraction fn  arc cosine fn  arc sine fn  arc tangent fn  back fn  begin fn  begin node fn  cardinality fn  ceiling fn  complement fn  cosine fn  cut set fn  denominator fn  end fn  end node fn  extension fn  floor fn  front fn  future fn  generalized intersection fn  generalized union fn  giga fn  imaginary part fn  immediate future fn  immediate past fn  integer square root fn  kilo fn  list length fn  magnitude fn  mega fn  micro fn  milli fn  minimal cut set fn  nano fn  numerator fn  organization fn  past fn  path weight fn  pico fn  power set fn  predecessor fn  principal host fn  probability fn  property fn  rational number fn  real number fn  reciprocal fn  round fn  signum fn  sine fn  skin fn  square root fn  successor fn  tangent fn  tera fn  terminal node fn  wealth fn  when fn  year fn

## Type restrictions

graph node InitialNodeFn(graph arc)

## Axioms (4)

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))))```

```(=>
(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 "the starting node of arc" is equal to node and "the terminal node of arc" is equal to node, then arc is an instance of graph loop.
```(=>
(and
(equal
(InitialNodeFn ?ARC)
?NODE)
(equal
(TerminalNodeFn ?ARC)
?NODE))
(instance ?ARC GraphLoop))```

begin node fn is internally related to initial node fn.
`(relatedInternalConcept BeginNodeFn InitialNodeFn)`