Trying to create a pulse process model from an adjacency matrix

Hello, I am a new MATLAB user- like brand new... so the more in depth (an layman's terms used) description the better.

I created a digraph conceptual model and then turned it into a matrix and would like to run a pulse process model on the matrix to see if it has stability and by what vertex is the model most effected? I'd also kind of like to figure out an eigenvalue for the matrix, but it is a huge matrix and contains many 0's.

Anyone smart out there understand what I mean and want to give it a shot? I'd be super appreciative.

Thanks,

Ash