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# begin node fn (BeginNodeFn)

A UnaryFunction that maps a GraphPath to the GraphNode that is the beginning of the GraphPath. Note that, unlike InitialNodeFn (which relates a GraphArc to a GraphNode), BeginNodeFn is a total function - every GraphPath has a beginning.

## Ontologie

SUMO / GRAPH-THEORY

## Class(es)

 třída

inheritable relation

unární funkce

begin node fn

## Související termín(y)

absolute value fn  abstraction fn  arc cosine fn  arc sine fn  arc tangent fn  back fn  begin 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  initial node 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

## Typy argumentů

uzel grafu BeginNodeFn(cesta v grafu)

## Axiomy (3)

Jestliže graph je instancí třídy graf a node1 je instancí třídy uzel grafu a node2 je instancí třídy uzel grafu a node1 je částí graph a node2 je částí graph a node1 se nerovná node2, potom existují arc,path tak, že
```(=>
(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)))))))```

graph je instancí třídy cyklus tehdy a jen tehdy pokud existuje node tak, že "the beginning of graph" se rovná node a "the end of graph" se rovná node.
```(<=>
(instance ?GRAPH GraphCircuit)
(exists
(?NODE)
(and
(equal
(BeginNodeFn ?GRAPH)
?NODE)
(equal
(EndNodeFn ?GRAPH)
?NODE))))```

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