Functions to construct graphs- see details below.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
knn_graph(g, k = 2)
dn_graph(g, d = 1, test=`<=`)
mk_binary_graph(n,sep="",delta=1,test=`==`)
mk_hypercube_graph(n,sep="")
mk_line_graph(g,sep="-")
kspace_graph(n,m, link=NULL,sep="-")
graph_product(g,h, type="cartesian",sep="-")
graph_compose(g,h,sep="-")
graph_sum(g,h,combineWeight=`+`)
bipartite_graph(n1,n2)
iterated_line_graph(g,sep="-")
``` |

`g` |
a graph |

`h` |
a graph |

`n` |
a positive integer, or a character vector. |

`k` |
a positive integer |

`d` |
an edge weight |

`test` |
used to select edges. |

`sep` |
used to form node names of new graph. |

`m` |
subsets of size m are nodes of kneser graph. |

`link` |
A positive number or NULL. If NULL, the returned graph is complete. Otherwise edges for subsets sharing link elements. |

`type` |
the type of graph product, one of "cartesian", "strong" or "tensor" |

`n1` |
a character vector. |

`n2` |
a character vector. |

`delta` |
used to select edges. |

`combineWeight` |
used to combine weights. |

knn_graph- returns a symmetric k nearest neighbour graph

dn_graph- returns a graph formed from g where edges of satisfy test(weight, d). The default retains edges whose weight are 1 are less. Nodes with no edges are also removed.

mk_hypercube_graph- returns a hypercube graph with $2^n$ nodes

mk_binary_graph(n,sep="",delta=1,test='==') - returns a graph with $2^n$ nodes. Undirected edges join nodes A and B whose binary vectors satisfy *a_i ≤q b_i$,$i=1, …, n* and test(*∑(b_i - a_i)*, delta) is true.

mk_line_graph- returns the line graph of g

kspace_graph- returns a graph where nodes are subsets of size m from n. Edges are connect nodes whose subsets share link elements. The standard kneser graph has link=0. When link is NULL, returned graph is complete.

graph_product(g,h, type="cartesian",sep="-")- returns the graph product of g and h.

graph_compose(g,h,sep="-")- returns the graph composition of g and h.

bipartite_graph(n1,n2)- returns the complete bipartite graph with node sets n1 and n2.

graph_sum(g,h,combineWeight='+')- returns a graph whose nodes and edges are the union of those in g and h. Weights of common edges are combined using combineWeight.

iterated_line_graph- returns the iterated line graph of g, with compression of nodes as described in the reference Hurley and Oldford(2008) given below.

C.B. Hurley and R.W. Oldford

See any Graph Theory text. Also C.B. Hurley and R.W. Oldford, Graphs as navigational infrastructure for high dimensional data spaces. 2008 submitted.

1 2 | ```
# See the demo file nav.R
``` |

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