PAlocationmodel <- function(startconf = list(degree = c(1,1), location = c(1/3,2/3)), size = 100000, alpha = -3/4, locprofile = c(0,1,0)){
  #Samples the Preferential attachment model with location-based choice
  #Parameters:
  #startconf    - list of vertices of the initial graph G_0, containing their initial degree and their location in arrays. 
  #             To ensure, that the initial graph is a tree, check the sufficient and necessary condition that the sum of the degrees is equal to 2*(number of vertices - 1)
  #size         - number of vertices added to the graph
  #alpha        - parameter controlling the importance of the degree in the preferential attachment mechanism.
  #locprofile   - probability vector which describes the connection mechanism to one of the selected vertices
  
  #Generating location for all vertices
  startnumber = length(startconf$degree);
  startdegree = sum(startconf$degree);
  vertices = list(degree = c(startconf$degree,rep(0,size)), location = c(startconf$location, runif(size)))
  
  #Connecting new vertices to the model
  for (i in 1:size){
    #Selecting vertices due to Preferential Attachment
    sumdegree = startdegree + alpha*startnumber + (2+alpha)*(i-1);    #Calculating the normalizing constant of Psi. Assuming the startconfiguration has a tree structure: sumdegree = (2+alpha)*((i-1)+startnumber) - 2 
    sampleid = sample(1:((i-1)+startnumber), size = length(locprofile), replace = TRUE, prob =  (vertices$degree[1:((i-1)+startnumber)] + alpha)/sumdegree )
    samplevert = list(name = sampleid, degree = vertices$degree[sampleid], location = vertices$location[sampleid]);
    
    #Order sample with respect to the location of the vertex
    sortind = sort(samplevert$location, index.return = TRUE)
    samplevert = list(name = samplevert$name[sortind$ix], degree = samplevert$degree[sortind$ix], location =  samplevert$location[sortind$ix])
    
    #Choose one vertex of the ordered sample according to the given probability vector and connect to this one
    connectid = sample(samplevert$name, size = 1, prob = locprofile)
    vertices$degree[i + startnumber] = 1;
    vertices$degree[connectid] = vertices$degree[connectid] + 1;
    if(i %% 100000 == 0){print(i)}
  }
  return(vertices)
}