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| 1 | """ | |
| 2 | Do your friends have more friends than you? | |
| 3 | - | It's not you. It's statistics. |
| 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) |
