arXiv subjects

Gonzalo Contreras-Aso

Publications and source records attributed to Gonzalo Contreras-Aso.

6 recordsLinked to original sources

arXiv2025

Equitability and explosive synchronisation in multiplex and higher-order networks

Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units. However, it is not known under which conditions equitability-induced synchronisation is the only cluster synchronisation that can occur on a particular system. Here, we reveal a natural linear independent condition such that equitability becomes necessary, and sufficient, for the existence of cluster synchronised solutions on a very general dynamical system which allows multiplex or higher-order, arbitrarily weighted interactions. Our results explain the ubiquity of explosive synchronisation, as opposed to cluster synchronisation, in multiplex and higher-order networks: equitability imposes additional constraints that must be simultaneously satisfied on the same set of nodes. Our results have significant implications for the design of complex dynamical systems of coupled dynamical units with arbitrary cluster synchronisation patterns and coupling functions.

nlin.AO↗

arXiv2025

Fully personalized PageRank and algebraic methods to distribute a random walker

We present a comprehensive analysis of algebraic methods for controlling the stationary distribution of PageRank-like random walkers. Building upon existing literature, we compile and extend results regarding both structural control (through network modifications) and parametric control (through measure parameters) of these centralities. We characterize the conditions for complete control of centrality scores and the weaker notion of ranking control, establishing bounds for the required parameters. Our analysis includes classical PageRank alongside two generalizations: node-dependent dampings and node-dependent personalization vector, with the latter being a novel idea in the literature. We examine how their underlying random walk structures affect their controllability, and we also investigate the concepts of competitors and leaders in centrality rankings, providing insights into how parameter variations can influence node importance hierarchies. These results advance our understanding of the interplay between algebraic control and stochastic dynamics in network centrality measures.

cs.SI↗

arXiv2024

Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities

The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of heterogeneous hypergraphs from an algebraic point of view, which have traditional directed hypergraphs as a particular case. We furthermore analytically study the spectral centralities associated to some types of heterogeneous hypergraphs, extending previously defined eigenvector-like centrality measures to this new realm. We supplement the analytical arguments with some numerical comparisons of pairwise and higher order rankings, and we construct directed higher order networks from real data.

math-ph↗

arXiv2024

Uplifting edges in higher order networks: spectral centralities for non-uniform hypergraphs

Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is strongly limited by the fact that a given hypergraph could have several different adjacency hypermatrices, hence the results obtained so far are mainly restricted to the class of uniform hypergraphs, which leaves many real systems unattended. A new method for analysing non-linear eigenvector-like centrality measures of non-uniform hypergraphs is presented in this paper that could be useful for studying properties of $\mathcal{H}$-eigenvectors and $\mathcal{Z}$-eigenvectors in the non-uniform case. In order to do so, a new operation - the $\textit{uplift}$ - is introduced, incorporating auxiliary nodes in the hypergraph to allow for a uniform-like analysis. We later argue why this is a mathematically sound operation, and we furthermore use it to classify a whole family of hypergraphs with unique Perron-like $\mathcal{Z}$-eigenvectors. We supplement the theoretical analysis with several examples and numerical simulations on synthetic and real datasets.

math.SP↗

arXiv2024

The transition to synchronization of networked systems

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network's nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.

physics.soc-ph↗

arXiv2023

Can the PageRank centrality be manipulated to obtain any desired ranking?

The significance of the PageRank algorithm in shaping the modern Internet cannot be overstated, and its Complex Network theory foundations continue to be a subject of research. In this article we carry out a systematic study of the structural and parametric controllability of PageRank's outcomes, translating a spectral Graph Theory problem into a geometric one, where a natural characterization of its rankings emerges. Furthermore, we show that the change of perspective employed can be applied to the biplex PageRank proposal, performing numerical computations on both real and synthetic network datasets to compare centrality measures used.

physics.soc-ph↗