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As you have certainly seen now, I like working on artificial neural networks. I have written a few posts about models with neural networks (Models to generate networks, Want to win to Guess Who and Study of spatial segregation).**ProbaPerception**, and kindly contributed to R-bloggers)Unfortunately, I missed so far a nice and pleasant aspect of networks : its graphical approach. Indeed, plots of neural networks are often really nice and really useful to understand the network.

Sometimes such a graph can point out some characteristics of the network. For example, we see in the graph below that there is one "central" node linked with many other nodes. It would not be that obvious if we were looking at a simple print() of a network matrix!

So if you like this representation, let me introduce you to the package network.

Let's first download the package and use a home-made function to generate networks randomly (if you want to see more details about this function, see here):

install.packages('network')

library(network)

generateBA = function(n = 100, n0 = 2){

mat = matrix(0, nrow= n, ncol = n)

for(i in 1:n0){

for(j in 1:n0){

if(i != j){

mat[i,j] = 1

mat[j,i] = 1

}

}

}

for(i in n0:n){

list = c()

for(k in 1:(i-1)){

list = c(list, sum(mat[,k]))

}

link = sample(c(1:(i-1)), size = 1, prob = list)

mat[link,i] = 1

mat[i,link] = 1

}

return(mat)

}

artificialNet= generateBA(200)

To create an object network from a matrix, the package uses the function network():

a = network(artificialNet, directed = FALSE)

# The parameter directed is specified as FALSE because in our case, artificialNet is a symetrical matrix.

# It is really convenient to plot a nice network

plot(a)

#plot.network() is the function to use if we want to change some parameters

There are many other useful function in this package. Let's start with the function to study the properties of the network. We can compute the density of the network ("The density of a network is defined as the ratio of extant edges to potential edges."), the number of nodes and the number of edges.

network.density(a)

network.size(a)

network.size(a)

network.edgecount(a)

Besides, this package offers the possibility to create and manage operations on the object network. The function network.initialize(n) creates a network with n nodes and no edges.

net = network.initialize(10)

plot(net)

Adding a edge (and therefore define our whole network) is then really simple :

net[1,2] = 1

plot(net)

But the real power of this package is in the definition of operators. Here are the operators (source : the library) :

**+**: An (i; j) edge is created in the return graph for every (i; j) edge in each of the input graphs.

matched by an (i; j) edge in the second input; if the second input has more (i; j) edges than

the first, no (i; j) edges are created in the return graph.

**- :**An (i; j) edge is created in the return graph for every (i; j) edge in the first input that is notmatched by an (i; j) edge in the second input; if the second input has more (i; j) edges than

the first, no (i; j) edges are created in the return graph.

*****: An (i; j) edge is created for every pairing of (i; j) edges in the respective input graphs.

in the first input and the second edge in the second input.

**%c%**: An (i; j) edge is created in the return graph for every edge pair (i; k); (k; j) with the first edgein the first input and the second edge in the second input.

**!**: An (i; j) edge is created in the return graph for every (i; j) in the input not having an edge.

**|**: An (i; j) edge is created in the return graph if either input contains an (i; j) edge.

**&**: An (i; j) edge is created in the return graph if both inputs contain an (i; j) edge.These operators enable to do some really convenient operations between two networks.

If you want to find more information about this wonderful package, you can read the pdf of the package.

To

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