# Graph Centrality: spectral techniques

What is the difference between:

• normalizing the row of an adjacency matrix and taking the right eigenvector
• normalizing the row of an adjacency matrix and taking the left eigenvector
• normalizing the columns of an adjacency matrix and taking the right eigenvector
• normalizing the columns of an adjacency matrix and taking the left eigenvector

I think that if you take the left eigenvector (number of paths coming INTO a node) you should normalize the COLUMNS, while if you are interested in the RIGHT eigenvector (number of paths outgoing from a node) you should normalize the ROWS.

Why is l1 norm used?

Thank you :)

• 1. Why is this a question about computer science? This seems like a pure mathematics question (suitable for Math.SE). Can you articulate the connection to computer science or why you think computer scientists are likely to have special expertise in answering this question? 2. What have you tried? Have you tried working through some examples? We expect you to make a significant effort on your own before asking, and to show us in the question what you've tried. 3. Normalized how? 4. L1 norm? Used, for what? How could we possibly know, without some context? – D.W. Apr 5 '15 at 0:07
• You are right. I was just too much into the context to see it. I'm studying graph centrality algorithms, so I'm talking about the isomorphism between graph and matrices, where normalization means that you have a stochastic matrix (L1 norm it's used because it must sum up to 1, I forgot it..) that rapresent a Markov Process. – asdf Apr 9 '15 at 23:04