Scale-Free NetworksBrett J. Janecek and Kate Kenehan

“How can systems as fundamentally different as the cell and the internet

have the same architecture and obey the same laws?”

- ALBERT-LASZLO BARABASI AND ERIC BONABEAU

NetworksVarious Complex Systems

• Randomly Distributed Networks– roots in the work of two Hungarian mathematicians, Paul

Erdos and Alfred Renyi– Nodes organized in a Poisson distribution with a bell

shape– Resulting system democratic

• Scale-free Networks– Discovered during a project to map the World Wide Web

• by Albert-Laszlo Barabasi, Eric Bonabeau, Hawoong Jeong and Reka Albert of the University of Notre Dame

– Hubs• Make system surprisingly resistent to accidental

errors• Still vulnerable to planned and coordinated attacks

Mapping of these systems

• Imagery aids comprehension of the organization of complex networks

Category: Internet Topology Description: Internet connectivity snapshot

using Skitter data and Walrus visualization

Category: Natural NetworksDescription: Yeast protein network map, inside

cell

Category: Natural NetworksDescription: Portion of food web in North Atlantic Ocean

Category: Social NetworksDescription: Science co-authorship network

from the Max Planck Institute

Category: Social NetworksDescription: Individuals and their professions in the network of activities during the German Revolution of

1848-1849

Category: Economic Networks

Description: World Trade network, 1992

HIV/AIDS

•Social Networks are Free-Scale

•HIV/AIDS spreads rapidly

•Nodes Need to be eliminated

•Ethical Issues

The Facebook

Coordinated Attacks

•Hackers can plan attacks

•Free-Scale susceptible

•WWW can be destroyed

•What happens then?

We Live in Hovels like Hobbits

Some might think that would be fun!

Was Barabasi the First?

Thank you for your time!

Sources

• Text:– “Scale-Free Networks,” Albert-Laszlo Barabasi and Eric

Bonabeau, Scientific American, May 2003

• Images:– http://www.jeffkennedyassociates.com:16080/connectio

ns/concept/image.html– Google Image Search