Dynamics on Accelerated Growth Tree Networks: Random Walks and Consensus Problem

It is of great interest to create theoretical models that certainly show some structural properties observed on real-world networks and to study dynamics occurring on models. In this paper, we first propose a principled framework for constructing accelerated growth networks, with which we generate four families of growth tree networks [Formula: see text] for instance where [Formula: see text]. Among which, tree networks [Formula: see text] and [Formula: see text] are built in the vertex-based accelerated uniform growth way, and the other two tree networks are created in the edge-based accelerated uniform growth manner. Then, we consider two classes of dynamics, i.e., random walks and consensus problem, on the proposed models. Specifically, we derive an exact solution to mean hitting time [Formula: see text] for random walks on trees [Formula: see text], and find that the proposed trees all possess efficient underlying structure because the correspondingly analytic expression for quantity [Formula: see text] can be very close to the theoretical lower bound in the limit of large graph size. Also, the first-order noise coherence [Formula: see text] for consensus problem on trees [Formula: see text] is derived analytically. Lastly, we not only execute extensive simulations, demonstrating that empirical analysis is consistent with theoretical results, but also provide the guideline to create random tree networks based on the proposed framework to highlight its own wide range of applicability.