from IPython.display import Image
Image('w4.png')

mweb={1:[2,3],2:[3],3:[1],4:[3]}

T= array([[1./len(mweb[i]) if m in mweb[i] else 0. for m in mweb] for i in mweb])
T

around(reduce(dot,[T]*25),3)

p=.2
n=len(T)
Tp=p*ones([n,n])/n + (1-p)*T

Tp

linalg.matrix_power(Tp,8)

(1/4.)*ones(4).dot(linalg.matrix_power(Tp,8))