1
00:00:00,000 --> 00:00:03,864
Hi. Welcome back. We're in our last
lecture on networks. Remember we've talked

2
00:00:03,864 --> 00:00:07,679
about the structure of networks. Things
like their degree, their path length,

3
00:00:07,679 --> 00:00:11,594
their clustering coefficient, and we
talked about the logic on network's form.

4
00:00:11,594 --> 00:00:15,815
In this lecture we're gonna talk about the
functionality of that structure. So, when

5
00:00:15,815 --> 00:00:19,578
a network has some structure to it, it has
some degree distribution, it has

6
00:00:19,578 --> 00:00:23,291
connectedness, it has a clustering
coefficient, and what we can ask is, how

7
00:00:23,291 --> 00:00:27,461
do those properties of that network allow
it to carry out different functions? Now

8
00:00:27,461 --> 00:00:31,122
remember when we think about those
functions, they're typically emerging.

9
00:00:31,122 --> 00:00:34,460
When people form an. But they're not
thinking about the entire network. They're

10
00:00:34,460 --> 00:00:38,432
just thinking about their own connections.
So those properties the network structure

11
00:00:38,432 --> 00:00:42,525
itself just emerges from the logical
process through which it forms and we

12
00:00:42,525 --> 00:00:46,778
wanna talk about how that structure. Has
functionality so it can do particular

13
00:00:46,778 --> 00:00:51,194
things. We're gonna start out by talking
about something known as the six degrees

14
00:00:51,194 --> 00:00:55,393
phenomenon. And let me explain where this
comes from. It comes from two famous

15
00:00:55,393 --> 00:00:59,864
experiments in social science. So Stanley
Milgram, in the'60s, asked 296 people from

16
00:00:59,864 --> 00:01:04,159
Nebraska to get a letter to a stockbroker
in Boston. Now, the rule is, they could

17
00:01:04,159 --> 00:01:08,593
only send the letter to someone they knew
on a first name basis. And what he found

18
00:01:08,593 --> 00:01:12,757
is that, on average, of the letters that
got there, it took about six steps. Now,

19
00:01:12,757 --> 00:01:16,974
Duncan Watts, you know, almost 40 years
later, redid this experiment with 48,000

20
00:01:16,974 --> 00:01:21,246
people on the internet. And they had to
send an email to someone they knew on a

21
00:01:21,246 --> 00:01:25,096
first name basis. And try to get it
eventually to these. You know, target

22
00:01:25,096 --> 00:01:29,424
people all around the globe. And what he
found, again, that the average number of

23
00:01:29,424 --> 00:01:33,752
steps was six. So it took, typically, six
steps to get from one person to another.

24
00:01:33,752 --> 00:01:38,354
So there's this six degrees phenomena that
we want to understand how that can be. So

25
00:01:38,354 --> 00:01:42,256
we're gonna do this. By looking at a
variant of the Small World's network. So

26
00:01:42,256 --> 00:01:46,415
we know that social networking have that
small world structure to that. We're gonna

27
00:01:46,415 --> 00:01:50,524
use that to explain how you can get six
degrees of separation. So when people form

28
00:01:50,524 --> 00:01:54,633
friendship networks, they don't do it with
the intent of creating a six degrees of

29
00:01:54,633 --> 00:01:58,742
separation world network. We're gonna show
that it just emerges from the structure.

30
00:01:58,742 --> 00:02:02,801
So we're gonna start off by simplifying
the small world network as follows. We're

31
00:02:02,801 --> 00:02:06,860
gonna assume that each person has a group
friends, see if them belong to a clique.

32
00:02:06,860 --> 00:02:10,768
[inaudible] gonna be friends with each
other and then you've got a few random

33
00:02:10,768 --> 00:02:15,694
friends off. To this side. So you get C
click friends and R random friends. Let me

34
00:02:15,694 --> 00:02:19,656
show what this looks like. So, here's a
clique, and everybody within the clique

35
00:02:19,656 --> 00:02:23,656
we're gonna assume is friends with
everybody else. So, it's got a very high

36
00:02:23,656 --> 00:02:27,872
clustering coefficient, and then each
person in the clique also has one random

37
00:02:27,872 --> 00:02:32,359
friend, and that random friend belongs to
some other clique. Now I need to introduce

38
00:02:32,359 --> 00:02:36,088
a [inaudible] idea. This is called a K
neighbor. So, a one neighbor is someone

39
00:02:36,088 --> 00:02:40,041
that you're connected to. So that's be a
one neighbor. A two neighbor is someone

40
00:02:40,041 --> 00:02:43,462
who's connected to someone you're
connected to. And a three neighbor is

41
00:02:43,462 --> 00:02:47,365
someone who's connected to someone who's
connected to someone who's connected to

42
00:02:47,365 --> 00:02:51,220
you. So what you get is you're three steps
away. Now, if there's also a connection

43
00:02:51,220 --> 00:02:54,978
between these two people, so this person
is both one step away, and three steps

44
00:02:54,978 --> 00:02:58,640
away, we would classify them as a one
neighbor. So that the shortest distance

45
00:02:58,640 --> 00:03:02,398
between one person and another. So your
three neighbors are the people who are

46
00:03:02,398 --> 00:03:05,909
three steps away, but they're not two
steps away, or one step away. So six

47
00:03:05,909 --> 00:03:10,134
degrees of separation is going to mean
that someone is six steps away, but not

48
00:03:10,134 --> 00:03:14,413
five, four, three, two, or one. So let me
show this graphically, I'm looking at this

49
00:03:14,413 --> 00:03:18,475
person here, the one neighbors are going
to be the two people he's directly

50
00:03:18,475 --> 00:03:21,993
connected to. The two neighbors aren't
gonna include these two people he's

51
00:03:21,993 --> 00:03:25,867
directly connected to but it will include
these two people who are connected to the

52
00:03:25,867 --> 00:03:29,674
people. He's connected to. So one
neighbors are who you're connected to. Two

53
00:03:29,674 --> 00:03:33,166
neighbors that were connected to people
we're connected to. That's the idea. Now

54
00:03:33,166 --> 00:03:37,539
we're gonna use this to show how you can
get six degrees of separation. Here's how

55
00:03:37,539 --> 00:03:41,965
it works. If you look at a person in this
random clique network, what they've got is

56
00:03:41,965 --> 00:03:46,124
they've got, who are their one neighbors?
It's their clique friends, which we'll

57
00:03:46,124 --> 00:03:50,443
represent by this C. And then their random
friends, which we'll represent as being

58
00:03:50,443 --> 00:03:54,679
red. Those are the one neighbors. Now, who
are the two neighbors? Well, their two

59
00:03:54,679 --> 00:03:59,762
neighbors are their click friends. Random
friends, that's these people. Their random

60
00:03:59,762 --> 00:04:04,286
friends, random friends, which are these
two people. And then, finally, their

61
00:04:04,286 --> 00:04:09,244
random friends, click friends, which are
these people. So all I've done is they've

62
00:04:09,244 --> 00:04:13,774
got quick friends and random friends, I've
just sort of written all of this stuff

63
00:04:13,774 --> 00:04:17,914
out. What about [cough]? What about the
click friends, click friends? Well, my

64
00:04:17,914 --> 00:04:22,501
click friends are just equal to my click
friends so if I think about how I get my

65
00:04:22,501 --> 00:04:26,975
two neighbors I just click friend. Random,
random, random click but I don't add in

66
00:04:26,975 --> 00:04:31,455
click, click because those are just the
click friends. All right? What about the

67
00:04:31,455 --> 00:04:35,435
three neighbors. Well, I do the same
thing. I've got my random friends, random

68
00:04:35,435 --> 00:04:39,203
friends, random friends, my random
friends, random friends, random friends,

69
00:04:39,203 --> 00:04:43,342
click friends right? My random friends,
click friends, random friends, so who are

70
00:04:43,342 --> 00:04:47,481
my random friends, click friends, random
friends? So I'm going to click. I've got

71
00:04:47,481 --> 00:04:51,727
some random friends. My random friends
belong to a click and then I've got their

72
00:04:51,727 --> 00:04:55,578
click friends. Random friends, that's who
these people are. So I could just write

73
00:04:55,578 --> 00:04:58,974
down all possible combinations.
[inaudible] random clique, clique random,

74
00:04:58,974 --> 00:05:02,849
random, random clique, that sort of thing.
However, I can't write down random clique,

75
00:05:02,849 --> 00:05:06,675
clique. 'Cause if I have two cliques in a
row, my random friends, [inaudible] I've

76
00:05:06,675 --> 00:05:10,550
got a random friend, and he's in a clique,
my random friend's clique friends, which

77
00:05:10,550 --> 00:05:14,041
are these people, well, their clique
friends are the same people. So random

78
00:05:14,041 --> 00:05:17,533
clique, clique is the same [inaudible]
random, as random clique. And clique,

79
00:05:17,533 --> 00:05:21,098
clique random is the same as clique
random. And clique, clique, clique. It's

80
00:05:21,098 --> 00:05:25,273
just my seamed clique. So what I have to
do is write out all these combinations and

81
00:05:25,273 --> 00:05:29,297
that gives me the total number of three
names. Well let's do this in a real case.

82
00:05:29,297 --> 00:05:33,169
So, let's take I've got 140 clique friends
and ten random friends. And this is

83
00:05:33,169 --> 00:05:36,942
actually approximately the number of
friends that people might have. People

84
00:05:36,942 --> 00:05:41,016
have about 150 friends, most are sort of
close to you. So, let's compute the number

85
00:05:41,016 --> 00:05:45,406
of one neighbors. Well that's just equal
to 150. What about the number of two

86
00:05:45,406 --> 00:05:50,089
neighbors? Well, I've got my clique
friends, random friends. My random

87
00:05:50,089 --> 00:05:55,400
friends, clique friends. And my random
friends, random friends. So that's gonna

88
00:05:55,400 --> 00:06:00,782
be, got 140 clique friends, and each has
ten random friends. So that's gonna be

89
00:06:00,782 --> 00:06:06,093
1,400. I've got ten random friends, each
one has 140 clique friends. So that's

90
00:06:06,093 --> 00:06:13,382
another 1,400. And then I've got. Ten.
Random friends each of whom has ten random

91
00:06:13,382 --> 00:06:19,353
friends. So that give me another 100,
which gives me 2900. I add all that up.

92
00:06:19,353 --> 00:06:24,960
So, I've got 151 neighbors, I've got 2,902
neighbors. What about three neighbors?

93
00:06:24,960 --> 00:06:29,775
Well, here I've got random, random,
random, random, random, click, random,

94
00:06:29,775 --> 00:06:35,800
click, random. End click random, random.
And then click random click. Those are all

95
00:06:35,800 --> 00:06:41,199
the possibilities. So if I do this, I'm
gonna get ten times ten times ten, which

96
00:06:41,199 --> 00:06:46,752
is 1000. I'm gonna get ten times ten times
140, which is gonna be 14,000, that's a

97
00:06:46,752 --> 00:06:52,922
lot. I'm gonna get another random click
random, so that's another 14,000. And I've

98
00:06:52,922 --> 00:06:59,351
got this, which is another 14,000. And
then here, I've got 140. Times ten, which

99
00:06:59,351 --> 00:07:07,044
is 1,400 times. 140, which is gonna give
me 1-4-0-0-0. And then I'm gonna get +56,

100
00:07:07,044 --> 00:07:14,478
excuse me, 196,000. So when I add all this
together, I'm gonna get 229,000 three

101
00:07:14,478 --> 00:07:21,626
neighbors, so that's a lot. [laugh]. I've
got 229, 000 three neighbors. 150 one

102
00:07:21,626 --> 00:07:28,168
neighbors. 2,902 neighbors, 229,000. Three
neighbors, that's interesting. It's

103
00:07:28,168 --> 00:07:31,486
interesting, cuz it help us understand a
phenomena that's been long known

104
00:07:31,486 --> 00:07:35,213
empirically. So, in 1973, Mark [inaudible]
wrote a paper called The Strength of Weak

105
00:07:35,213 --> 00:07:38,940
Ties. And what he found in this paper is,
if you think of the important things that

106
00:07:38,940 --> 00:07:42,577
happen in your life, like the job you get,
who you marry, where you live. All sorts

107
00:07:42,577 --> 00:07:46,304
of important things. It doesn't depend on
your one neighbors, your close friends. It

108
00:07:46,304 --> 00:07:50,122
tends to come from your three and your two
neighbors and your three neighbors. These

109
00:07:50,122 --> 00:07:53,577
weak ties, these people who you're
remotely connected to, end up having a big

110
00:07:53,577 --> 00:07:57,122
effect on your life. Well, let's think
about who these three neighbors are. So a

111
00:07:57,122 --> 00:08:00,697
three neighbor could be your roommate's
brother's friend, right. One, two. Three

112
00:08:00,697 --> 00:08:05,045
Could be your mother's co-worker's
daughter. One two three or could be your

113
00:08:05,045 --> 00:08:09,566
high school roommate's college roommate's,
dad. You know one two three so three

114
00:08:09,566 --> 00:08:13,924
[inaudible] aren't that far away and
actually can seem [inaudible]. Points of,

115
00:08:13,924 --> 00:08:17,194
sort of, interesting story. Like, I
actually got a job with my roommate,

116
00:08:17,194 --> 00:08:20,891
brother's friend. He hired me for his
firm. It doesn't seem that far-fetched. In

117
00:08:20,891 --> 00:08:24,589
fact, it's not far-fetched because, as
Granovetter shows, that's how most people

118
00:08:24,589 --> 00:08:28,087
get jobs. Why does that happen? Well,
let's look. Remember, we've got. 151

119
00:08:28,087 --> 00:08:35,610
neighbors, 2902 neighbors, and 229,003
neighbors. There's so many more. Of these

120
00:08:35,610 --> 00:08:39,394
three neighbors, that their just that much
more likely to get you the job. They're

121
00:08:39,394 --> 00:08:43,132
also that much more likely to introduce
you to the person you're going to marry.

122
00:08:43,132 --> 00:08:47,056
They're also that much more likely to tell
you about a great new place to live or a

123
00:08:47,056 --> 00:08:50,654
place to go on vacation. It's just the
sheer numbers. So, this puzzle, this sort

124
00:08:50,654 --> 00:08:54,438
of strength of weak ties puzzle, the study
that sort of loose connections get you

125
00:08:54,438 --> 00:08:58,409
things isn't a puzzle once we write down a
model and do a little bit math. Let's look

126
00:08:58,409 --> 00:09:02,240
at other network structures. So, here's a
network of collaboration among scientists,

127
00:09:02,240 --> 00:09:06,156
collaborations among scientists. I want
you to see that. These, that there's some

128
00:09:06,156 --> 00:09:10,757
people who collaborate more with others.
They're more central to the production of

129
00:09:10,757 --> 00:09:15,142
knowledge. And if we think back to our.
Internet model, or worldwide web model, we

130
00:09:15,142 --> 00:09:19,151
saw that we got that power law
distribution. So there was some nodes that

131
00:09:19,151 --> 00:09:23,545
were connected to a lot. And they were,
most nodes were connected to few. What are

132
00:09:23,545 --> 00:09:27,445
the functionalities of this sort of
network? Look, here's an interesting

133
00:09:27,445 --> 00:09:31,675
functionality. Suppose I think about
random node failures. So suppose nodes on

134
00:09:31,675 --> 00:09:36,289
the internet are gonna fail randomly. Well
most nodes are connected to very few. Most

135
00:09:36,289 --> 00:09:40,848
nodes are over here. So that means if you
have random failure, this node is gonna be

136
00:09:40,848 --> 00:09:45,091
incredibly robust. So no one said, hey,
let's. Make connections in such a way that

137
00:09:45,091 --> 00:09:49,326
makes the internet robust, but the fact
that it emerges from the structure of the

138
00:09:49,326 --> 00:09:53,299
network. What about targeted failures?
What if you want to shut down internet?

139
00:09:53,299 --> 00:09:57,272
What if you want to target failure, then
you go after these, lots and lots of

140
00:09:57,272 --> 00:10:01,611
connections. So although the internet is
really robust in handling failure but it's

141
00:10:01,611 --> 00:10:05,741
not at all robust to targeted failure.
That's a functionality that emerges from

142
00:10:05,741 --> 00:10:09,990
the preferential [inaudible] rule. Nobody
built them in. They just happened. So what

143
00:10:09,990 --> 00:10:13,793
have we learned? We learned that it's sort
of fun to talk about networks. There's

144
00:10:13,793 --> 00:10:17,596
pictures but we can really unpack it in a
formal way by constructing models and

145
00:10:17,596 --> 00:10:21,352
networks. Cause models and networks can
focus on the logic. How does the network

146
00:10:21,352 --> 00:10:25,132
form. The structure. What are the
statistical properties within networks?

147
00:10:25,132 --> 00:10:29,157
And then finally the functionality. What
does the network do? Right. Does the

148
00:10:29,157 --> 00:10:33,720
network robust to random failures or is it
robust to strategic failures? Does it give

149
00:10:33,720 --> 00:10:37,853
us six degrees of separation or 400
degrees of separation? Is it connected or

150
00:10:37,853 --> 00:10:41,663
non-connected? So there's all these
functionalities that emerge from the

151
00:10:41,663 --> 00:10:45,491
network structure. And the network
structure in turn is a result of. The

152
00:10:45,491 --> 00:10:49,371
individual logic for how people make
connections, or how firms make

153
00:10:49,371 --> 00:10:53,757
connections, or how. Web pages make
connections. [laugh]. One last thing,

154
00:10:53,757 --> 00:10:58,147
before I conclude this set of lectures on
networks. Now that we have networks we

155
00:10:58,147 --> 00:11:02,536
understand the functionality of those
networks. We can think about interventions

156
00:11:02,536 --> 00:11:06,652
into the network. So here's, again, a
social network that suppose you want to

157
00:11:06,652 --> 00:11:11,151
ask that there's some disease that's going
to spread. Now remember we talked about

158
00:11:11,151 --> 00:11:15,870
our model of vaccinations and you see that
you have to vaccinate as a function of the

159
00:11:15,870 --> 00:11:20,424
R0 so the higher R0 is the more people you
have to vaccinate. But that was assuming

160
00:11:20,424 --> 00:11:24,111
that people were randomly connected. And
then, everybody's sort of, randomly

161
00:11:24,111 --> 00:11:27,624
meeting other people. But in real social
networks, you'll see there's some like

162
00:11:27,624 --> 00:11:31,137
this person here, and these people here,
that are much more central to the node.

163
00:11:31,137 --> 00:11:34,592
M-, much more central to the graph.
They're connected to lots of people. These

164
00:11:34,592 --> 00:11:38,277
might be schoolteachers, these might be
bus drivers. So if you think about

165
00:11:38,277 --> 00:11:42,012
vaccination, rather than saying, okay,
blanket. We've got to vaccinate twenty

166
00:11:42,012 --> 00:11:45,292
percent of people or 30 percent of people,
based on R zero. Instead, you could look

167
00:11:45,292 --> 00:11:49,128
at the social network and say, oh, you
know what? We needed to vaccinate these

168
00:11:49,128 --> 00:11:53,065
people, these people, these people, these
people. So by profession, [inaudible] by

169
00:11:53,065 --> 00:11:57,102
profession, who are the most important
people to vaccinate to prevent this thing

170
00:11:57,102 --> 00:12:01,200
from spreading? So by combining our
network model with our disease [inaudible]

171
00:12:01,200 --> 00:12:05,496
model, we can actually come up with lower
vaccination rates to stop the spread of

172
00:12:05,496 --> 00:12:09,845
diseases. So again, this is why you wanna
be a many model thinker. Cuz if you've got

173
00:12:09,845 --> 00:12:14,193
lots of models in your head, you can then
combine those models in interesting ways.

174
00:12:14,193 --> 00:12:18,329
So we have the vaccination model, which
says, the more virulent the disease, the

175
00:12:18,329 --> 00:12:22,081
more people we have to vaccinate. Now
we've got this network model says, well,

176
00:12:22,081 --> 00:12:25,896
no, everybody's not connected to everybody
with equal probability. The random graph

177
00:12:25,896 --> 00:12:29,666
model isn't true of social networks. So
then you realize, that what really matters

178
00:12:29,666 --> 00:12:33,110
isn't vaccinating everybody, but
vaccinating the key people to prevent the.

179
00:12:33,110 --> 00:12:37,383
Disease from spreading. And what you'd
like to do is make the network, by

180
00:12:37,383 --> 00:12:42,310
snipping off people, disconnected. Because
if it's disconnected then it can't spread.

181
00:12:42,310 --> 00:12:46,000
Okay, so we've learned a lot about
networks, their logic, their structure,

182
00:12:46,000 --> 00:12:50,375
and their function. And we've seen how we
can [inaudible] for the disease model. But

183
00:12:50,375 --> 00:12:54,698
if we take a lot of the models we've done
in class, you can also throw networks in.

184
00:12:54,698 --> 00:12:59,021
So a lot of research has been done in the
last 10-15 years in social sciences, has

185
00:12:59,021 --> 00:13:03,133
been to add networks onto things, like
economic performance, school performance,

186
00:13:03,133 --> 00:13:07,404
things like that, to show how these sort
of interactions between individuals have

187
00:13:07,404 --> 00:13:10,778
an effect on what's happening at the macro
level. Alright, thanks.