Description Usage Arguments Details Value Author(s) See Also Examples

View source: R/edgefunctions.R

For any graph a set of nodes can be used to obtain an induced subgraph
(see `subGraph`

). An interesting question is whether that
subgraph has an unusually large number of edges. This function
computes the probability that a *random* subgraph with the same
number of nodes has more edges than the number observed in the
presented subgraph. The appropriate probability distribution is
the hypergeometric.

1 | ```
calcSumProb(sg, g)
``` |

`sg` |
subgraph made from the original graph |

`g` |
original graph object from which the subgraph was made |

The computation is based on the following argument. In the original
graph there are *n* nodes and hence *N=n*(n-1)/2* edges in the
complete graph. If we consider these *N* nodes to be of two types,
corresponding to those that are either in our graph, `g`

, or not in
it. Then we think of the subgraph which has say *m* nodes and
*M=m*(m-1)/2* possible edges as representing *M* draws from an
urn containing *N* balls of which some are white (those in `g`

)
and some are black. We count the number of edges in the subgraph and use
a Hypergeomtric distribution to ask whether our subgraph is particularly
dense.

The probability of having greater than or equal to the subgraph's number of edges is returned.

Elizabeth Whalen

1 2 3 4 5 6 | ```
set.seed(123)
V <- letters[14:22]
g1 <- randomEGraph(V, .2)
sg1 <- subGraph(letters[c(15,17,20,21,22)], g1)
calcSumProb(sg1, g1)
``` |

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