The topology of real network was shaped by many effect like

1. The topology of real network was shaped by many effect like • All links present in the scale free model are added when new nodes join the network, in most network new links can emerge spontaneously. • In many network nodes and links can disappear. Indeed ,many web pages go out of business, taking with them thousands of links. • Links can also be rewired.

2. Luis Amaral, a research professor at Boston university demonstrated that • If nodes fail to acquire links after a certain age the size of the hubs will be eliminated, making large hubs less frequent than predicted by a power law. • Assuming that nodes slowly lose their ability to attract as they age Mendes and Dorogovtsev showed that gradual aging does not destroy power laws , but merely alters the number of hubs by changing the degree exponent.

3. Paul Krapivsky and Sid Redner from Boston university found that linking to a node would not be simply proportional to the number of links the node has but would follow some more complicated function. They also found that such effect can destroy the power law characterizing the network.

4. The eighth legacy Einstein’s legacy

5. Google launched in 1997, was a latecomer to the web. • It violated the basic prediction of the scale-free model, that the first mover has an advantage. • It became the both the biggest node and the most popular search engine.

6. In a competitive environment each node has a certain fitness • Fitness is a quantitative measure of a node’s ability to stay in front of the competition • Nodes with higher fitness are linked more frequently. • Between two nodes with the same number of links, the fitter one acquires links more quickly. • If two nodes have the same fitness, the older one has an advantage

7. Independent of when a node joins the network , a fit node will soon leave behind all nodes with smaller fitness • e.g. Google a late comer with great searching technology acquired links much faster than its competitors