# specialg: Functions to construct graphs. In PairViz: Visualization using Eulerian tours and Hamiltonian decompositions

## Description

Functions to construct graphs- see details below.

## Usage

 ``` 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="-") ```

## Arguments

 `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.

## Details

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.

## Author(s)

C.B. Hurley and R.W. Oldford

## References

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

## Examples

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

PairViz documentation built on May 29, 2017, 12:23 p.m.