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Social networks 
John Bradford, Ph.D.
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.
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.)
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
‘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
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
SIX DEGREES OF SEPARATION 
• We are just 6 degrees of separation from 
everyone on the planet!
Networks are like… 
• Our influence spreads 
through our social 
networks like 
– Ripples in a pond, or 
– Movements on a spider’s 
web.
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
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
Spread of Emotions in Social 
Networks 
• EMOTIONS are contagious! 
• Laughter epidemic in Tanzania, 1962…
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.
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.
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%
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
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
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
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
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
Map of World Happiness 
Note: The happiest country on earth is Denmark!
CLIQUES 
• A CLIQUE is a network in which everyone is 
connected to everyone else.
Small Worlds 
• Small-worlds = short average distance 
between unconnected people.
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.
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)
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.
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.
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.
Strong and Weak Ties 
• Our ‘weak ties’ act as bridges. They connect 
us to other groups of people we would not 
know otherwise.
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.
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
‘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.

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TOPIC 4 Social 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.

Hinweis der Redaktion

  1. Note: “links” are also called ‘edges.’
  2. Note: “links” are also called ‘edges.’
  3. Questions: ‘who do you discuss important matters with’, ‘who do you spend your free time with?’ Average American has 4 close social contacts. 12% Americans said they have no one they could spend time with; 5% said 8. our core discussion network decreases as we age. No difference between women and men. E.g. homophily: Literally, “love of being alike” Hells Angels, Jehovah’s witnesses, coffee drinkers, drug addicts, stamp collectors, Republicans….
  4. How is ‘happiness’ measured? Life satisfaction is typically measured with the following question: All things considered, how satisfied are you with your life as a whole these days?
  5. Note that growth alone will favor the older nodes, even if the links are randomly selected, since all nodes have a chance to link to the oldest nodes. “Seniority, however, is not sufficient to explain the power laws” (87).