TY - JOUR

T1 - Hierarchical deposition and scale-free networks

T2 - A visibility algorithm approach

AU - Berx, Jonas

N1 - Funding Information: The author is grateful for the spirited discussions with J. O. Indekeu and R. Tielemans, whose insights were very enlightening, and for the suggestions received from L. Lacasa. He also acknowledges the support of the G-Research grant. Publisher Copyright: © 2022 American Physical Society.

PY - 2022/12

Y1 - 2022/12

N2 - The growth of an interface formed by the hierarchical deposition of particles of unequal size is studied in the framework of a dynamical network generated by a horizontal visibility algorithm. For a deterministic model of the deposition process, the resulting network is scale free with dominant degree exponent γe=ln3/ln2 and transient exponent γo=1. An exact calculation of the network diameter and clustering coefficient reveals that the network is scale invariant and inherits the modular hierarchical nature of the deposition process. For the random process, the network remains scale free, where the degree exponent asymptotically converges to γ=3, independent of the system parameters. This result shows that the model is in the class of fractional Gaussian noise through the relation between the degree exponent and the series' Hurst exponent H. Finally, we show through the degree-dependent clustering coefficient C(k) that the modularity remains present in the system.

AB - The growth of an interface formed by the hierarchical deposition of particles of unequal size is studied in the framework of a dynamical network generated by a horizontal visibility algorithm. For a deterministic model of the deposition process, the resulting network is scale free with dominant degree exponent γe=ln3/ln2 and transient exponent γo=1. An exact calculation of the network diameter and clustering coefficient reveals that the network is scale invariant and inherits the modular hierarchical nature of the deposition process. For the random process, the network remains scale free, where the degree exponent asymptotically converges to γ=3, independent of the system parameters. This result shows that the model is in the class of fractional Gaussian noise through the relation between the degree exponent and the series' Hurst exponent H. Finally, we show through the degree-dependent clustering coefficient C(k) that the modularity remains present in the system.

U2 - 10.1103/PhysRevE.106.064305

DO - 10.1103/PhysRevE.106.064305

M3 - Journal article

C2 - 36671195

AN - SCOPUS:85143880100

VL - 106

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 064305

ER -