A new paper on random walks on bifractal networks is available on arXiv.

My co-authored paper on random walks on bifractal networks is now available on arXiv!

In our last paper, we demonstrated that networks with scale-free and fractal properties often exhibit the structural bifractality, in which there exist two distinct local fractal dimensions. Our speculation from our previous result was that the bifractality of those networks may cause qualitative differences in dynamical processes on them from those on conventional networks. Hence, we examined, as one of the first example, random walks and studied the spectal and walk dimensions of random walks on bifractal networks.

Our primary finding is that the spectral dimension takes two distinct values due to the bifractality, while the walk dimension remains unaffected. Suprisingly, the smaller value of spectral dimension of random walks starting from the vicinity of hub nodes implies that the number of nodes reached by random walkers is greater when the walkers start from non-hub nodes distant from hub nodes.

If you are interested, please check out the paper from here!