The Science of Networks 3.1

Today’s topicsStrength of Weak Ties

Next TopicHow does Google rank webpages in search?

AcknowledgementsJames Moody, Alan Kirman, Dejan Vinkovic

The Science of Networks 3.2

Factors influencing diffusion

Network structure (unweighted) density degree distribution clustering connected components community structure

Strength of ties (weighted) frequency of communication strength of influence

Spreading agent attractiveness and specificity of information

The Science of Networks 3.3

How does strength of a tie influence diffusion? M. S. Granovetter: The Strength of Weak Ties,

AJS, 1973:

Finding a job through a contact that one saw frequently (2+ times/week) 16.7% occasionally (more than once a year but < 2x

week) 55.6% rarely 27.8%

But… length of path is short contact directly works for/is the employer or is connected directly to employer

The Science of Networks 3.4

Strength of Weak Ties

Why do leads for new jobs come from weak contacts?

What binds communities together?

How do ties afffect access to resources?

What are the social implications?

The Science of Networks 3.5

Strong ties

A strong tie frequent contact affinity many mutual contacts

Less likely to be a bridge (or a local bridge)

“forbidden triad”:

strong ties are likely to “close”

Source: Granovetter, M. (1973). "The Strength of Weak Ties", American Journal of Sociology, Vol. 78, Issue 6, May 1973, pp. 1360-1380.

The Science of Networks 3.6

Triadic Closure

The Science of Networks 3.7

Triadic Closure

The Science of Networks 3.8

Triadic Closure

The Science of Networks 3.9

Strength of ties on facebook

The Science of Networks 3.10

Strength of ties on Facebook

Why are some ties more common than others?

The Science of Networks 3.11

Strength of ties on twitter

Study by Wu, Golder & Huberman

The Science of Networks 3.12

What indicates cohesion?

Mutuality of ties everybody in the group knows everybody else

Closeness or reachability of subgroup members individuals are separated by at most n hops

Frequency of ties Among members

• everybody in the group has links to at least k others

• Among subgroup members compared to nonmembers

Why? Discover communities of practice Measure isolation of groups Threshold processes:

• I will adopt an innovation if some number of my contacts do

• I will vote for a measure if a fraction of my contacts do

The Science of Networks 3.13

Columbia Small World Experiment Identical protocol to Travers and Milgram,

but conducted via the Internet 60,000 participants from 170 countries

attempting to reach 18 different targets Results

Median “true” chain length 5 < L < 7 Successful chains disproportionately used

• professional ties (34% vs. 13%)• ties originating at work/college• target's work (65% vs. 40%)• weak ties (Granovetter)

. . . and disproportionately avoided• hubs (8% vs. 1%) (+ no evidence of funnels)• family/friendship ties (60% vs. 83%)