1. Rich get richer By: Eric Havens, Sanusha Matthews, and Mike Copciac

2. Old Network Assumptions • 1) Having all the nodes from the beginning, we assume that the number of nodes is fixed and remains unchanged throughout the network’s life. • 2) All nodes are equivalent • For nearly fourty years of network research these assumptions were unquestioned. The discovery of hubs and the power laws that describe them, forced us to abandon both assumptions.

3. Growth:the feature most networks have in common • If you look at any network you will likely see that starting with a few nodes, it grew incrementally through the addition of new nodes, gradually reaching its current size. • World Wide Web-started with only one node (website) which was by Tim Berners-Lee. Physicists and computer scientists started creating pages of their own and within 10 years there were thousands of websites. • Hollywood network- had only 53 actors in 1900 and has grown to over half a million.

4. Random Network vs. Preferential Attachment • Random Network • Choosing a news site off the internet- Yahoo’s directory offers over 8,000 news sources and each are equally likely to be chosen based on this theory. • Picking an actor for a role in a movie-each of the thousands of actors has an equal change of being chosen • Preferential Attachment • We choose big news outlets or the ones we are most familiar with. • A director chooses based on how well they fit the role and popularity. The ones that have been in the most movies are the most likely to be selected (rich get richer)

5. The Birth of A Scale-Free Network • From the two key concepts of growth and preferential attachment in networks the scale-free topology is a natural consequence of the continuously expanding nature of real networks. • When deciding where to link, new nodes prefer to attach to the more connected nodes. Due to growth and preferential attachment, a few highly connected hubs emerge.