# Generating undirected network with pre-specified degree distribution without any self loops

I would like to generate an undirected network with 100 nodes, where half of the nodes have a degree of 10 and the other half has a degree of 3. Is such a network possible to construct without self loops?

Using the code specified below:

```library(graph)
degrees=c(rep(3,50),rep(10,50))
names(degrees)=paste("node",seq_along(degrees)) #nodes must be names
x=randomNodeGraph(degrees)
```

I can obtain such a graph, but there are self-loops included.

Is there any way to get a graph without self loops?

It is easy to do with the graph package from Bioconductor (see here)

```#install graph from Bioconductor
source("http://bioconductor.org/biocLite.R")
biocLite("graph")

#load graph and make the specified graph
library(graph)
degrees=c(rep(3,50),rep(10,50))
names(degrees)=paste("node",seq_along(degrees)) #nodes must be names
x=randomNodeGraph(degrees)

#verify graph
edges=edgeMatrix(x)
edgecount=table(as.vector(edges))
table(edgecount)
#edgecount
# 3 10
#50 50
```

The Erdős–Gallai theorem answers the question if such a graph is possible to construct.

It is based on the non-decreasing degree sequence of your graph which is in your case

```ds <- c( rep( 10, 50 ), rep(3,50) )
```

You can calculate the right-hand side of the inequality by

```rhs <- (1:100 * 0:99) + c( rev(cumsum(rev(apply( data.frame(ds, 1:100) , 1, min ))))[-1], 0 )
```

And the left-hand side by

```lhs <- cumsum( ds )
```

Finally:

```all( lhs <= rhs )
[1] TRUE
```