How to translate an adjacency matrix to a transition matrix for use in Markov cluster algorithm? I have a matrix of size (47*47 double) that have only 0's and 1's.
I want to apply the Markov clustering algorithm on this matrix, but this Method needs a transition matrix as the columns must be normalized to sum to one.
Could anyone help me to turn this adjacency matrix into a transition matrix.
I appreciate any help!
here are the adjacency and the transition matrix I have
https://drive.google.com/open?id=0B6u8fZadKIp2bF9neFM5dmNnR0E
https://drive.google.com/open?id=0B6u8fZadKIp2bjdnVUNTWDMyUm8
 A: Adjacency matrix and transition matrix give different information. It's easy to come with a simple method to map valid adjacency matrices into valid transition matrices, but you need to make sure that the transition matrix you get fits your problem - that is, if the information that is in the transition matrix but wasn't in the adjacency matrix is true for your problem.
I understand that your problem deals with 47 different states, and that a directed graph can be build showing all possible transitions -that is, if state i can change to state j, an edge will be drawn from node i to node j- and that your adjacency matrix shows which edges are connected.
Therefore, your adjacency matrix shows which states the system can reach from any given one, but it doesn't show which is the probability to get to each one. That information will be encoded in the transition matrix and you need to know it or to make reasonable assumptions.
A simple assumption is that for any given state all possible transition have the same probability. Under this assumption you can compute the transition matrix by dividing every value in the adjacency matrix by the column sum - that is, making every column to sum 1. Anyway, beware that this simple assumption might not fit your problem.
Edit: From https://www.cs.ucsb.edu/~xyan/classes/CS595D-2009winter/MCL_Presentation2.pdf I see that assuming equal probabilities for every edge from the same node is the standard procedure.
