Exact results for the first-passage properties in a class of fractal networks

Abstract

In this work we consider a class of recursively-grown fractal networks $G_n(t)$, whose topology is controlled by two integer parameters $t$ and $n$. We first analyse the structural properties of $G_n(t)$ (including fractal dimension, modularity and clustering coefficient) and then we move to its transport properties. The latter are studied in terms of first-passage quantities (including the mean trapping time, the global mean first-passage time and the Kemeny's constant) and we highlight that their asymptotic behavior is controlled by network's size and diameter. Remarkably, if we tune $n$ (or, analogously, $t$) while keeping the network size fixed, as $n$ increases ($t$ decreases) the network gets more and more clustered and modular, while its diameter is reduced, implying, ultimately, a better transport performance. The connection between this class of networks and models for polymer architectures is also discussed.

arXiv comment14 pages, 4 figures

References in corpus (32)

• Statistical mechanics of complex networks
• Finding and evaluating community structure in networks
• Modularity and community structure in networks
• Human Mobility: Models and Applications
• Random walks and diffusion on networks
• First-passage times in complex scale-invariant media
• Geometry-controlled kinetics
• Diffusion, subdiffusion, and trapping of active particles in heterogeneous media
• First passage time for random walks in heterogeneous networks
• Exact mean first-passage time on the T-graph
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Random Walks on deterministic Scale-Free networks: Exact results
• Cancer-driven dynamics of immune cells in a microfluidic environment
• The Role of Kemeny's Constant in Properties of Markov Chains
• Exact calculations of first-passage quantities on recursive networks
• A Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories
• Explicit determination of mean first-passage time for random walks on deterministic uniform recursive trees
• Trapping in dendrimers and regular hyperbranched polymers
• Undestanding Baseball Team Standings and Streaks
• Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers
• Exact calculations of first-passage properties on the pseudofractal scale-free web
• Random Multi-Hopper Model. Super-Fast Random Walks on Graphs
• The two-particle problem in comb-like structures
• Anomalous behavior of trapping on a fractal scale-free network
• Scaling laws for diffusion on (trans)fractal scale-free networks
• Tree formulas, mean first passage times and Kemeny's constant of a Markov chain
• Hitting and Trapping Times on Branched Structures
• Efficiency analysis of diffusion on T-fractals in the sense of random walks
• Mean trapping time for an arbitrary node on regular hyperbranched polymers
• A stochastic approach for quantifying immigrant integration: the Spanish test case
• Analysis of fluctuations in the first return times of random walks on regular branched networks
• Effects of node position on diffusion and trapping efficiency for random walks on fractal scale-free trees