# graph.constructors

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##### Various methods for creating graphs

These method can create various (mostly regular) graphs: empty graphs, graphs with the given edges, graphs from adjacency matrices, star graphs, lattices, rings, trees.

Keywords
graphs
##### Usage
graph.empty(n=0, directed=TRUE)
graph(edges, n=max(edges), directed=TRUE)
graph.star(n, mode = c("in", "out", "mutual", "undirected"), center = 1)
graph.lattice(dimvector = NULL, length = NULL, dim = NULL, nei = 1,
directed = FALSE, mutual = FALSE, circular = FALSE, ...)
graph.ring(n, directed = FALSE, mutual = FALSE, circular=TRUE)
graph.tree(n, children = 2, mode=c("out", "in", "undirected"))
graph.full(n, directed = FALSE, loops = FALSE)
graph.full.citation(n, directed = TRUE)
graph.atlas(n)
graph.edgelist(el, directed=TRUE)
graph.extended.chordal.ring(n, w)
##### Arguments
edges
Numeric vector defining the edges, the first edge points from the first element to the second, the second edge from the third to the fourth, etc.
directed
Logical, if TRUE a directed graph will be created. Note that for while most constructors the default is TRUE, for graph.lattice and graph.ring it is FALSE. For graph.star the mode argument sh
n
The number of vertices in the graph for most functions.

For graph this parameter is ignored if there is a bigger vertex id in edges. This means that for this function it is safe to supply zero here if the vertex with

mode
For graph.star it defines the direction of the edges, in: the edges point to the center, out: the edges point from the center, mutual: a directed star is created with mutual
center
For graph.star the center vertex of the graph, by default the first vertex.
dimvector
A vector giving the size of the lattice in each dimension, for graph.lattice.
nei
The distance within which (inclusive) the neighbors on the lattice will be connected. This parameter is not used right now.
mutual
Logical, if TRUE directed lattices will be mutually connected.
circular
Logical, if TRUE the lattice or ring will be circular.
length
Integer constant, for regular lattices, the size of the lattice in each dimension.
dim
Integer constant, the dimension of the lattice.
children
Integer constant, the number of children of a vertex (except for leafs) for graph.tree.
loops
If TRUE also loops edges (self edges) are added.
graph
An object.
el
An edge list, a two column matrix, character or numeric. See details below.
w
A matrix which specifies the extended chordal ring. See details below.
...
Currently ignored.
##### Details

All these functions create graphs in a deterministic way.

graph.empty is the simplest one, this creates an empty graph.

graph creates a graph with the given edges.

graph.star creates a star graph, in this every single vertex is connected to the center vertex and nobody else.

graph.lattice is a flexible function, it can create lattices of arbitrary dimensions, periodic or unperiodic ones. It has two forms. In the first form you only supply dimvector, but not length and dim. In the second form you omit dimvector and supply length and dim.

graph.ring is actually a special case of graph.lattice, it creates a one dimensional circular lattice.

graph.tree creates regular trees.

graph.full simply creates full graphs.

graph.full.citation creates a full citation graph. This is a directed graph, where every i->j edge is present if and only if jdirected=FALSE then the graph is just a full graph. graph.atlas creates graphs from the book An Atlas of Graphs by Roland C. Read and Robin J. Wilson. The atlas contains all undirected graphs with up to seven vertices, numbered from 0 up to 1252. The graphs are listed:

1. in increasing order of number of nodes;
2. for a fixed number of nodes, in increasing order of the number of edges;
3. for fixed numbers of nodes and edges, in increasing order of the degree sequence, for example 111223 < 112222;
4. for fixed degree sequence, in increasing number of automorphisms.

graph.edgelist creates a graph from an edge list. Its argument is a two-column matrix, each row defines one edge. If it is a numeric matrix then its elements are interpreted as vertex ids. If it is a character matrix then it is interpreted as symbolic vertex names and a vertex id will be assigned to each name, and also a name vertex attribute will be added. graph.extended.chordal.ring creates an extended chordal ring. An extended chordal ring is regular graph, each node has the same degree. It can be obtained from a simple ring by adding some extra edges specified by a matrix. Let p denote the number of columns in the W matrix. The extra edges of vertex i are added according to column i mod p in W. The number of extra edges is the number of rows in W: for each row j an edge i->i+w[ij] is added if i+w[ij] is less than the number of total nodes. See also Kotsis, G: Interconnection Topologies for Parallel Processing Systems, PARS Mitteilungen 11, 1-6, 1993.

##### Value

• Every function documented here returns a graph object.

##### concept

• Tree
• Lattice
• Star graph
• Graph Atlas
• Empty graph
• Full graph

graph.adjacency to create graphs from adjacency matrices, graph.formula for a handy way to create small graphs, graph.data.frame for an easy way to create graphs with many edge/vertex attributes.

##### Aliases
• graph.constructors
• graph.empty
• graph
• graph.star
• graph.lattice
• graph.ring
• graph.tree
• graph.full
• graph.full.citation
• graph.atlas
• graph.edgelist
• graph.extended.chordal.ring
##### Examples
g1 <- graph.empty()
g2 <- graph( c(1,2,2,3,3,4,5,6), directed=FALSE )
g5 <- graph.star(10, mode="out")
g6 <- graph.lattice(c(5,5,5))
g7 <- graph.lattice(length=5, dim=3)
g8 <- graph.ring(10)
g9 <- graph.tree(10, 2)
g10 <- graph.full(5, loops=TRUE)
g11 <- graph.full.citation(10)
g12 <- graph.atlas(sample(0:1252, 1))
el <- matrix( c("foo", "bar", "bar", "foobar"), nc=2, byrow=TRUE)
g13 <- graph.edgelist(el)
g15 <- graph.extended.chordal.ring(15, matrix(c(3,12,4,7,8,11), nr=2))
Documentation reproduced from package igraph, version 0.7.1, License: GPL (>= 2)

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