Maximal entropy random walk: Difference between revisions

Revision as of 19:34, 11 November 2018

Revision as of 10:51, 2 December 2018

Line 46:

Analogously calculating probability distribution for two succeeding vertices, one obtains that the probability of being at the <math>i</math>-th vertex and next at the <math>j</math>-th vertex is

:<math>\frac{\psi_i A_{ij} \psi_j}{\sum\limits_{i'=1}^n \sum\limits_{j'=1}^n \psi_{i'} A_{i'j'} \psi_{j'}} = \frac{\psi_i A_{ij} \psi_j}{\psi A \psi^\top} = \frac{\psi_i A_{ij} \psi_j}{\lambda \psi^2}</math>.

for some constant <math>c</math>. Dividing by the probability of being at the <math>i</math>-th vertex, i.e. <math>\rho_i</math>, gives for the [[conditional probability]] <math>S_{ij}</math> of the <math>j</math>-th vertex being next after the <math>i</math>-th vertex

:<math>S_{ij} = \frac{A_{ij}}{\lambda} \frac{\psi_j}{\psi_i}</math>.