I found a golden website. The blog of Esteban Moro. He uses R to work on networks. In particular he has done a really nice code to make some great videos of networks. This post is purely a copy of his code. I just changed a few arguments to change colors and to do my own network.

To create the network, I used the  Barabási-Albert algorithm that you can find at the end of the post on the different algorithms for networks. Igraph is the library which has been used.

In order to make a video from the .png I used a software called Ffmpeg. It took me a bit of time to use it but you can find some tutorials on Internet.

Here is the kind of result you can expect :

The code (R) : 


n <- 300
data <- matrix(0, ncol = 3, nrow = n-1)
data[1,2] <- 1
data[1:(n-1),1] <- 2:n
data[, 3] <- 1:(n-1)
weight <- NULL
weight[1] <- 1
weight[2] <- 1
for(i1 in 2:(n-1)){
  link = sample(c(1:(i1)), size = 1, prob = weight)
  data[i1, 2] <- link
  weight[i1+1] <- 1
  weight[link] <- weight[link] + 1
}

install.packages("igraph")
library(igraph)

#generate the full graph
g <- graph.edgelist(as.matrix(data[,c(1,2)]),directed=F)
E(g)$time <- data[,3]

#generate a cool palette for the graph
YlOrBr <- c(hsv(0.925, 0.20, 0.7), hsv(0.925, 0.40, 0.7), hsv(0.925, 0.60, 0.7), hsv(0.925, 0.80, 0.7), hsv(0.925,1, 0.7))
YlOrBr.Lab <- colorRampPalette(YlOrBr, space = "Lab")
#colors for the nodes are chosen from the very beginning
vcolor <- rev(YlOrBr.Lab(vcount(g)))

#time in the edges goes from 1 to 300. We kick off at time 3
ti <- 3
#weights of edges formed up to time ti is 1. Future edges are weighted 0
E(g)$weight <- ifelse(E(g)$time < ti,1,0)
#generate first layout using weights.
layout.old <- layout.fruchterman.reingold(g,params=list(weights=E(g)$weight))


#total time of the dynamics
total_time <- max(E(g)$time)
#This is the time interval for the animation. In this case is taken to be 1/10
#of the time (i.e. 10 snapshots) between adding two consecutive nodes
dt <- 0.1
#Output for each frame will be a png with HD size 1600x900 :)
png(file="example%04d.png", width=1600,height=900)
nsteps <- max(E(g)$time)
#Time loop starts
for(ti in seq(3,total_time,dt)){
  #define weight for edges present up to time ti.
  E(g)$weight <- ifelse(E(g)$time < ti,1,0)
  #Edges with non-zero weight are in gray. The rest are transparent
  E(g)$color <- ifelse(E(g)$time < ti,"black",rgb(0,0,0,0))
  #Nodes with at least a non-zero weighted edge are in color. The rest are transparent
  V(g)$color <- ifelse(graph.strength(g)==0,rgb(0,0,0,0),vcolor)
  #given the new weights, we update the layout a little bit
  layout.new <- layout.fruchterman.reingold(g,params=list(niter=10,start=layout.old,weights=E(g)$weight,maxdelta=1))
  #plot the new graph
  plot(g,layout=layout.new,vertex.label="",vertex.size=1+2*log(graph.strength(g)),vertex.color=V(g)$color,edge.width=1.5,asp=9/16,margin=-0.15)
  #use the new layout in the next round
  layout.old <- layout.new
}
dev.off()
3

View comments

  1. I came across your blog post while doing research for a book on analysis. I really like your example here, but there is one typo in your code. In the plot() function, ',olor=V(g)$color,' clearly something is cut off.

    Also, I'm not sure what you're trying to do with the colors here. I would love to see what the full, correct code does.

    Thanks.

    --Doug--

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
    2. @Doug, it appears the missing text should read 'vertex.color=V(g)$color'. Probably a copy/paste glitch.

      Paul

      Delete

The financial market is not only made of stock options. Other financial products enable market actors to target specific aims. For example, an oil buyer like a flight company may want to cover the risk of increase in the price of oil.

I found a golden website. The blog of Esteban Moro. He uses R to work on networks. In particular he has done a really nice code to make some great videos of networks. This post is purely a copy of his code. I just changed a few arguments to change colors and to do my own network.

3

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).

1

I already talked about networks a few times in this blog. In particular, I had this approach to explain spatial segregation in a city or to solve the Guess Who? problem. However, one of the question is how to generate a good network.

The function apply() is certainly one of the most useful function. I was scared of it during a while and refused to use it. But it makes the code so much faster to write and so efficient that we can't afford not using it.

1

Have you ever played the board game "Guess who?".

If you want to choose randomly your next holidays destination, you are likely to process in a way which is certainly biased. Especially if you choose randomly the latitude and the longitude.

4

My previous post is about a method to simulate a Brownian motion. A friend of mine emailed me yesterday to tell me that this is useless if we do not know how to simulate a normally distributed variable.

The Brownian motion is certainly the most famous stochastic process (a random variable evolving in the time). It has been the first way to model a stock option price (Louis Bachelier's thesis in 1900).

1

The merge of two insurance companies enables to curb the probability of ruin by sharing the risk and the capital of the two companies.

For example, we can consider two insurance companies, A and B.

How to estimate PI when we only have R and the formula for the surface of a circle (Surface = PI * r * r)?

The estimation of this number has been one of the greatest challenge in the history of mathematics. PI is the ratio between a circle's circumference and diameter.

I was in a party last night and a guy was totally drunk. Not just the guy who had a few drinks and speaks a bit too loud, but the one who is not very likely to remember what he has done during his night, but who is rather very likely to suffer from a huge headache today.

I am currently doing an internship in England. Therefore, I keep alternating between French and English in my different emails and other forms of communication on the Internet. I have been surprised to see that some websites are able to recognize when I use French or when I use English.

The VIX (volatility index) is a financial index which measures the expectation of the volatility of the stock market index S&P 500 (SPX). The higher is the value of the VIX the higher are the expectations of important variations in the S&P 500 during the next month.

The Olympic Games have finished a couple of days ago. Two entire weeks of complete devotion for sport. Unfortunately I hadn’t got any ticket but I didn’t fail to watch many games on TV and internet.

Hello (New World!), 

My name is Edwin, I’m a 22 year-old French student in applied mathematics. In particular, I study probability, statistics and risk theory.

Blog Archive
Translate
Translate
Loading