# Math Model for world wide web

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• Jan 13th 2011, 12:59 PM
mathsohard
Math Model for world wide web
In hurry :( help please

The model of A and B considers the situation when a new node attaches to the existing network consisting of n nodes. This new node has m undirected links, meaning this is linked to m existing nodes in two directions. If the entire web is built up this way, then the mean number of links is 2m, The probability of attachment by this new node to any existing node that already has k links is KPk(n)/2m where Pk(n) is the fraction of nodes in the network of n nodes that have k links. So the number of nodes that gain one link by this additional node is m times this probability.

a. derive the counterpart of Nk(n+1) -Nk(n) =KPk-1(n)m/m+1 - (k+1)Pk(n)m/m+1 by arguing that its right-handed side should be
1/2*(k-1)Pk-1(n)-1/2KPk(n)

b. For a large network (n large), show that this reduces to
Pk/Pk-1 = K-1/K+2

c. Solve the first-order difference equation above by iteration and show that the solution is a constant times
Pk o( 1/(K+2)(K+1)(K)
Therefore, for large k it is a power law with y=3.