1. The small-world problem
Stanley
Milgram

2. Small world poses a math problem
The problem: How can a network be both
very small and very clustered?

3. A “thought experiment”
How does the world get small?

5. Small-world network
but

6. Implications Evidence? Needed networks that were
Undetectability of small world at local level
Small worlds should be ubiquitous
Evidence?
Anecdotes
Milgram’s experiment
Needed networks that were
fully mapped, scientifically interesting

7. Real networks are “small worlds”
LActual
LRandom
CActual
CRandom
Movie actors
3.65
2.99
0.79
Power grid
18.7
12.4
0.080
0.005
C.elegans
2.65
2.25
0.28
0.05
L = average degrees of separation; C = clustering coefficient

8. Functional significance
Faster spreading in small-world nets (viruses, information, fads)
Finding a job (“strength of weak ties”)
Grassroots movements, social change?