arXiv subjects

Eduardo M. K. Souza

Publications and source records attributed to Eduardo M. K. Souza.

5 recordsLinked to original sources

arXiv2026

Hierarchical localization in disordered Apollonian networks

We investigate localization properties of the Apollonian network (AN) in the presence of diagonal and off-diagonal disorder. By employing a site-resolved localization measure, we show that the localization degree is strongly dependent on the energy and tied to the hierarchical topology of the network. At the spectral edges, eigenstates are strongly localized on highly connected sites originating from previous generations, a behavior that persists under both disorder mechanisms. In contrast, around zero energy localization is associated with the lowest-degree sites. As disorder breaks the underlying C3 symmetry of the AN, it promotes spatial reconfiguration of these states while preserving their support on low-degree nodes. For diagonal disorder, localization is enhanced over a broad range of negative energies, whereas off-diagonal disorder induces weakening of localization in this region. Finally, we show that the hub dominates the spectral edges but has negligible contribution near the band center, indicating that its associated localized states are robust against disorder. These results highlight how topology and disorder jointly shape localization in complex networks.

cond-mat.dis-nn↗

arXiv2026

Chesapeake Bay Food Web: Robustness Analysis via Energy Cutoff in Complex Networks

The Chesapeake Bay, one of the largest estuaries in the United States, is an ecological system of great complexity and relevance. The food web is composed of thirty-six trophic components, all of which are functionally connected. In this work, the interactions among these components are numerically analyzed using complex network methods. An energy flow cutoff paradigm is applied to a weighted ecological network. The results reveal patterns characteristic of connectivity dynamics, evidencing both the initial robustness of the system and its tendency to fragmentation at higher values of the cutoff. From an applied perspective, the findings underscore the importance of conservation strategies that protect keystone species, such as carnivorous fish, which act as crucial connectors between the two main subnetworks. Although they are positioned at the top of the food web and are often assumed to be less critical to network stability, these species play a pivotal role in regulating populations of lower-level organisms, thereby maintaining the overall integrity of the ecosystem.

physics.bio-ph↗

arXiv2024

Random Apollonian networks with tailored clustering coefficient

We introduce a family of complex networks that interpolates between the Apollonian network and its binary version, recently introduced in [Phys. Rev. E \textbf{107}, 024305 (2023)], via random removal of nodes. The dilution process allows the clustering coefficient to vary from $C=0.828$ to $C=0$ while maintaining the behavior of average path length and other relevant quantities as in the deterministic Apollonian network. Robustness against the random deletion of nodes is also reported on spectral quantities such as the ground-state localization degree and its energy gap to the first excited state. The loss of the $2π/ 3$ rotation symmetry as a tree-like network emerges is investigated in the light of the hub wavefunction amplitude. Our findings expose the interplay between the small-world property and other distinctive traits exhibited by Apollonian networks, as well as their resilience against random attacks.

cond-mat.dis-nn↗

arXiv2023

Infinity increasing steps on the Collatz sequences

We intend to contribute to the Collatz dynamics problem by seeking to analyze the Collatz conjecture from the tree of numbers sequences. First, we show numerically that the distribution of odd numbers has an initial transient, and proceeds to a power law growth to its maximum. Second, using the formulation that uses only odd numbers, we present analytically a set of odd number sequences that is always increasing and can have an infinite number of terms.

math.GM↗

arXiv2022

Binary Apollonian networks

There is a well-known relationship between the binary Pascal's triangle and Sierpinski triangle in which the latter obtained from the former by successive modulo 2 additions on one of its corners. Inspired by that, we define a binary Apollonian network and obtain two structures featuring a kind of dendritic growth. They are found to inherit the small-world and scale-free property from the original network but display no clustering. Other key network properties are explored as well. Our results reveal that the structure contained in the Apollonian network may be employed to model an even wider class of real-world systems.

cond-mat.dis-nn↗