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  1. """
  2. Do your friends have more friends than you?
  3. It's not you.  It's the Friendship Paradox.
  4. Sample code that accompanies
  5. http://badmomgoodmom.blogspot.com/2013/01/self-learner-project-friendship.html
  6. Written 6 Jan 2013 by BMGM
  7. """
  8. import pylab
  9. import numpy
  10.  
  11. def pickNumFriends(nsubj, shape=3, scale=5, stretch=5):
  12.     """
  13.         nsubj: number of people/subjects in circle
  14.         numf: number of friends for each subject, drawn from a stretched
  15.         gamma distribution of default values (shape=4, scale=5, stretch=10)
  16.         If number of friends for a subject > nsub, selects another number
  17.         returns a list sorted in ascending order
  18.         This is in here for reference but use the newer
  19.         pickNumFriendsRecur instead.
  20.        
  21.     """
  22.  
  23.     if nsubj <= 0:
  24.         raise ValueError('Set size must be greater than 0')
  25.  
  26.     numf = [int(0.5+stretch*numpy.random.gamma(shape,scale)) for _ in range(nsubj)]
  27.     print "avg numf before check: ", float(sum(numf))/float(nsubj)
  28.  
  29.     for i in range(nsubj):
  30.         while numf[i] > nsubj-1 :
  31.             numf[i] = int(0.5+10*numpy.random.gamma(shape,scale))
  32.  
  33.     print "Avg numf after size check: ", float(sum(numf))/float(nsubj)
  34.     # there should be only a slight difference, if any
  35.     # otherwise, increase the nsubj, reduce stretch, or change shape, scale
  36.    
  37.     return(pylab.sort(numf))
  38.  
  39. def pickNumFriendsRecur(nsubj, shape=2, scale=5, stretch=5):
  40.     """
  41.         nsubj: number of people/subjects in circle
  42.         numf: number of friends for each subject, drawn from a stretched
  43.         gamma distribution of default values (shape=4, scale=5, stretch=10)
  44.         if max(numf) > nsubj, reduces scale factor
  45.         and tries again, recursively, until not true
  46.         returns a list sorted in ascending order
  47.        
  48.     """
  49.  
  50.     if nsubj <= 0:
  51.         raise ValueError('Set size must be greater than 0')
  52.  
  53.     numf = [int(0.5+stretch*numpy.random.gamma(shape,scale)) for _ in range(nsubj)]
  54.  
  55.     if max(numf) > nsubj:
  56.         print "max(numf) > nsubj: ", max(numf), nsubj
  57.         print "trying reducing scale to: ", scale - 0.1
  58.         numf = pickNumFriendsRecur(nsubj, shape, scale-0.1, stretch)
  59.         print "avg numf after iteration: ", float(sum(numf))/float(nsubj)
  60.  
  61.     #pylab.hist(numf,20)
  62.     #pylab.show()
  63.    
  64.     return(pylab.sort(numf))
  65.  
  66. def assignFriends(numf):
  67.     """
  68.         Given the list of the number of friends per subject,
  69.         returns a list of lists of the friends for each subject
  70.     """
  71.     import random
  72.     nsubj = len(numf)
  73.     friendList = [[] for _ in range(nsubj)]
  74.     toofew = 0
  75.     factual = []
  76.    
  77.     for i in range(nsubj):
  78.         #print "i, numf, friendstart: ", i, numf[i], friendList[i]
  79.         # number of friends left to assign
  80.         npick = numf[i] - len(friendList[i])
  81.         pool = range(i+1, nsubj)
  82.        
  83.         #print "nleft to pick, len(pool), pool: ", nleft, len(pool), pool
  84.         if npick <= len(pool):
  85.             newfriends = random.sample(set(pool),npick)
  86.         else: # Not enough left in the pool.  Assigning all remaining"
  87.             toofew += 1
  88.             newfriends = pool
  89.             # Then randomly pick some more from earlier rejections
  90.             nleft = npick - len(newfriends)
  91.             reluctant = random.sample(set(range(i)), nleft)
  92.             newfriends += reluctant
  93.            
  94.         #print friends
  95.         friendList[i] += newfriends
  96.        
  97.  
  98.         for f in newfriends: # newfriends friend back
  99.             friendList[f].append(i)
  100.  
  101.     for i in range(nsubj):
  102.         factual.append(len(friendList[i]))
  103.    
  104.     print "Target average friends: ", sum(numf)/float(nsubj)
  105.     print "Adusted average assigned friends: ", sum(factual)/float(nsubj)
  106.  
  107.     pylab.title("Distribution of # Friends\nAverage number of friends: "+str(sum(factual)/float(nsubj)))
  108.     p1 = pylab.hist(factual,bins=range(0,500,10), label="After")
  109.     p2 = pylab.hist(numf, bins=range(0,500,10), histtype = 'step', label="Before Adjustment", linewidth=3)
  110.     #pylab.legend([p2,p1],["Before adjustment","After"])
  111.     pylab.show()
  112.    
  113.     return friendList
  114.  
  115. def howMany(flist):
  116.     """
  117.     How many friends do your friends have, on average?
  118.     And how does that compare to the number you have?
  119.     """
  120.     numfof = []
  121.     numf = []
  122.  
  123.     for i in range(len(flist)):
  124.         numf.append(len(flist[i]))
  125.         ifof = 0
  126.         for j in flist[i]:
  127.             ifof += len(flist[j])
  128.         avgfof = float(ifof)/len(flist[i])
  129.         numfof.append(avgfof)
  130.  
  131.     #print "Average friends: ", float(sum(numf))/len(flist)
  132.     print "Average friends of friends: ", float(sum(numfof))/len(flist)
  133.  
  134.     pylab.title("Friendship Paradox")
  135.     pylab.xlabel('Person')
  136.     pylab.ylabel('# Friends')
  137.     p1 = pylab.plot(numf, "bo", label="# Friends")
  138.     p2 = pylab.plot(numfof, "ro", label="# F of F")
  139.     pylab.legend()
  140.     pylab.show()
  141.  
  142.     return numfof
  143.  
  144. numf = pickNumFriendsRecur(500, shape=3, stretch=8)
  145. flist = assignFriends(numf)
  146. fof = howMany(flist)
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