networks

1. Social networks
John Bradford, Ph.D.

2. Explanations of Homophily
1. SORTING - e.g. happy people tend to attract
other happy people, etc.
2. CONFOUNDING INFLUENCES – common or
shared environmental influences.
– Example: a McDonald’s opens and everyone
nearby gains weight.
3. ** Peer Influence **
• These slides will focus on the causal influences
that people have on one another both directly
and indirectly across social networks.

3. Network Fundamentals
• A Network (sometimes called a
‘graph’) consists of:
1. nodes and
2. ‘Ties’ (aka links or ‘edges’)
connecting them.
• Nodes are things (people,
computers, countries, etc.)
• Ties are relationships between
the nodes (friendships, trading
agreements, boundaries, etc.)

4. Networks
Advanced/Optional
• A network is ‘connected’ if you can get
from one node to any other node.
– Example: Alaska is not ‘connected’ to the
lower 48 states.
• Path length: minimum number of links
you’d have to cross to get from one node to
another.
– Average path length: average of all path
lengths between all nodes.
• Degree of a node: the number of links that
connect to it
– Average degree of a network: sum of all
the links divided by the number of nodes.
– Average degree of states is 4: on average,
each state connects to 4 others.
Connected network
Dis-connected network

5. ‘RULES’ OF NETWORKS
• RULE 1: WE SHAPE OUR NETWORK
• RULE 2: OUR NETWORK SHAPES US
• RULE 3: OUR FRIENDS AFFECT US
• RULE 4: OUR FRIENDS’ FRIENDS’ FRIENDS
AFFECT US
– Hyper-dyadic spread
• RULE 5: THE NETWORK HAS A LIFE OF ITS
OWN.
– Emergence

6. SIX DEGREES OF SEPARATION
• In the 1960s, a few hundred people in
Nebraska were asked to send a letter to a
businessman in Boston, someone they
didn’t know and a thousand miles away.
• They were asked to send the letter to
somebody they knew personally, who they
thought might know someone who would
know the businessman. They would then
forward the letter to somebody they knew
personally, and so on, until the letter
arrived in Boston.
• In 2002, this experiment was replicated by
Duncan Watts, globally, using email.
Stanley Milgram
Duncan Watts

7. SIX DEGREES OF SEPARATION
• We are just 6 degrees of separation from
everyone on the planet!

8. Networks are like…
• Our influence spreads
through our social
networks like
– Ripples in a pond, or
– Movements on a spider’s
web.

9. 3 Degrees of Influence
• We are connected to everybody else (on
average) by 6 degrees of separation.
• But our influence extends to about 3 degrees.
1 degree
2 degrees
3 degrees

10. Types of Influence
• DIRECT, aka DYADIC
• Dyad = a pair. A dyad
consists of two nodes.
• Dyadic spread =
influence between two
people; within a dyad.
• INDIRECT, aka HYPER-DYADIC
• Hyperdyadic spread =
influence from node to
another node with 2 or
more degrees of
separation.
EXAMPLE: RUMORS, VIRUSES

11. Spread of Emotions in Social
Networks
• EMOTIONS are contagious!
• Laughter epidemic in Tanzania, 1962…

12. Spread of Emotions in Social
Networks
• People ‘catch’ emotional states they observe in
others.
• We are biologically hard-wired to mimic others outward
expressions; when we do so, we also mimic their inner
emotional states.
– College freshmen who are randomly assigned to live with
mildly depressed roommates become increasingly
depressed over 3 months.
– Strongest paths are from daughters to both parents,
while parents’ emotional states had no effect on their
daughters. (??)
– Father’s emotions affected wives and sons, but not
daughters.

13. Obesity is contagious!
• If a mutual friend becomes obese (fat), it triples a person’s
risk of becoming obese!
• Mutual friends are twice as influential as the friends
people name who do not name them back.
• There’s no effect at all by others who name them as
friends if they do not name them back.
3x RISK, or 300% increase
MUTUAL FRIENDS: BOTH NAME
THE OTHER AS A CLOSE FRIEND
150% increase
Not influenced by A
NON-MUTUAL FRIENDS: PERSON A
NAMES PERSON B AS A FRIEND, BUT
PERSON B DOES NOT NAME PERSON A.

14. Dyadic Influence:
Happiness Effect
• For each happy friend you have, your chance
of being happy increases by 9%.
• Each unhappy friend decreases it by 7%.
+9%
-7%
+9%
YOU
+9%

15. 3 Degrees of Influence:
Happiness Effect
• If you are happy…
– 1st degree: your close friends are 15% more likely to be happy.
– 2nd degree: your friends’ friends are 10% more likely to be
happy
– 3rd degree: your friends’ friends’ friends are 6% more likely to
be happy.
15%
10%
6%
YOU

16. 3 Degrees of Influence:
Happiness Effect
• Compare this effect to having more money:
an extra $5,000 associated with only a 2%
increased chance of a person being happy!
15%
10%
6%
YOU

17. 3 Degrees of Influence:
Happiness Effect
• People with more friends of friends who are
happy are also more likely to be happy
compared to people with the same amount of
friends, but with fewer friends of friends.
A B

18. 3 Degrees of Influence:
Happiness Effect
• Person A has the same amount of friends as person B.
• Person A has more friends of friends.
• Person A is more likely to be happy than person B.
A
B
3 FRIENDS
9 FRIENDS OF FRIENDS
3 FRIENDS
3 FRIENDS OF FRIENDS

19. 3 Degrees of Influence:
Loneliness effect
• 1st degree: you are 52% more likely to be lonely
if you are directly connected to a lonely person
• 2nd degree: 25% more likely
• 3rd degree: 15% more likely
52%
25%
15%
YOU

20. Map of World Happiness
Note: The happiest country on earth is Denmark!

21. CLIQUES
• A CLIQUE is a network in which everyone is
connected to everyone else.

22. Small Worlds
• Small-worlds = short average distance
between unconnected people.

23. Small Worlds
• A small-world is a social network in which most nodes
are not neighbors of one another, but most nodes can
be reached from every other by a small number of
hops or steps.
– Small worlds have low average path lengths between any
two (randomly selected) people.
– For example: 6 degrees of separation.

24. Small Worlds
• Small worlds are made by connecting
separated cliques with weak ties.
– A clique of friends (strong ties) is connected to
other cliques by one members’ acquaintances
(weak ties)

25. Small Worlds
Optional/Advanced
• To Build a Small World network,
1. begin with a circle of nodes, each of which have 2 links to
their nearest neighbors (a regular network).
2. Select a node and link it to another randomly selected node.
• Whereas in a regular network, the path length (= average
‘degrees of separation’) between nodes increases with
network size, in small worlds, the average path length
remains low, and clustering (cliques) remains high.

26. Strong and Weak Ties
• In 1973, Mark Granovetter’s article “The
Strength of Weak Ties” showed that most
people got their current jobs through
acquaintances (i.e. “weak ties”) rather than
close friends.
• Weak ties are our bridge to the outside world.

27. Strong and Weak Ties
• Why are we so
connected???
• ‘Strong Ties’ = “close ties”-
close relationships (family,
friends).
• ‘Weak Ties’ = “distant”
ties- acquaintances;
neighbors, people we
don’t know as well.

28. Strong and Weak Ties
• Our ‘weak ties’ act as bridges. They connect
us to other groups of people we would not
know otherwise.

29. Hub and Spokes Networks
• Many social networks do not resemble small worlds,
and instead look like ‘hub and spokes’ networks: a
few nodes called HUBS have disproportionately many
links, while most nodes called SPOKES only have a
few links, connected mostly to the hubs.

30. Hub and Spokes vs Random Network
Optional/Advanced
• The degree distribution of a random network follows a bell curve, telling us
that most nodes have the same number of links, and nodes with a very large
number of links don’t exist. A random network is similar to a national
highway system, whereas a “scale-free” hub and spokes network is similar
to an air traffic system. A few nodes have most of the links.
Highway system Air traffic system

31. ‘Externalities’
• ‘Externalities’ refer to the ‘side-effects’ of a
social interaction affecting people not directly
involved (‘3rd parties’).
– Externalities = indirect influences.
– Positive Externalities are beneficial indirect effects.
– Negative Externalities are harmful indirect effects.