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 Gn(t) whose topology is controlled by two integer parameters, t and n. We first analyse the structural properties of Gn(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 Kemeny’s constant), and we highlight that their asymptotic behavior is controlled by the 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 01, 2019
- Source ID
- 10.1063/1.5080481
Entities
People
- Elena Agliari
- Junhao Peng
Organizations
- Boston University
- Defense Threat Reduction Agency
- Guangzhou University
- Istituto Nazionale di Alta Matematica Francesco Severi
- National Natural Science Foundation of China
- National Science Foundation
- Sapienza University of Rome