python_functions

import networkx as nx
from numpy import random as rd
import numpy as np

def computeZfromGraph(seeds,G,a=0.01,b=0.1):
    
  def f(G,seeds,z):
    
    k=0.
    for seed in seeds:
      H=nx.DiGraph(G)
      y1=G.node[seed]['fitness']
      H.remove_node(seed)
      for j in H.nodes():
             y2=G.node[j]['fitness']
             k+=z*y1*y2/(1+z*y1*y2)  
      k+=-nx.Graph(G).degree()[seed]
    
    return k
    
  if sum(nx.degree(G,seeds).values())==0:
      return 0.
      
  f_a=f(G,seeds,a)
  f_b=f(G,seeds,b)
  
  count=0
  while f_a*f_b>0 and count<=100: 
       count+=1
       if f_a>0:
          b=a 
          a/=10.
       if f_a<0:
          a=b
          b*=10.
       f_a=f(G,seeds,a)
       f_b=f(G,seeds,b)
  
  c=(a+b)/2    
  while (b-a)>pow(10,np.log(c)/np.log(10.)-2):
      c=(a+b)/2
      if f(G,seeds,c)==0.:
        return c
      else:
        if f(G,seeds,c)*f(G,seeds,a)<=0:
           b=c
        if f(G,seeds,c)*f(G,seeds,b)<=0:
           a=c
    
  return c
  
  
def fitModelz(G,z):
 
         H=G.nodes()
         l=G.nodes()
         G0=nx.Graph()
         G0.add_nodes_from(G)
                   
         for i in l:
           H.remove(i)
           G0.node[i]['fitness']=G.node[i]['fitness']
           y1=G.node[i]['fitness']
           for j in H:
              y2=G.node[j]['fitness']
              p_i_j=z*y1*y2/(1+z*y1*y2)
              coin=rd.binomial(1, p_i_j)
              if coin==1 and (not G0.has_edge(i,j)):
                 G0.add_edge(i,j) #a ogni link un peso uguale
         
         return G0