Topologically biased random walks on graphs and the structure of complex networks

 

ANDREA GABRIELLI

NATIONAL RESEARCH COUNCIL (CNR), ROME, ITALY

 

We present a new approach of topology biased random walks for undirected networks. We consider a one parameter family of biases and present formal analogy with perturbation theory in quantum mechanics to investigate the related behavior random walks. This analogy is extended through the use of parametric equations of motion (PEM) to study the features of random walks in the parameter space. Finally we show an analysis of the location of the spectral gap maximum associated to the value of the second eigenvector. We provide also some hints to generalize this technique to more general bias (edge based strategies or mixed ones).