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. Duncan Watts

Stanley Milgram

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 degree2 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

NON-MUTUAL FRIENDS: PERSON ANAMES PERSON B AS A FRIEND, BUTPERSON B DOES NOT NAME PERSON A.

Not influenced by 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%

YOU

+9%

+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.

AB

3 FRIENDS9 FRIENDS OF FRIENDS

3 FRIENDS3 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 WorldsOptional/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 NetworkOptional/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.