March 14, 2022

Pablo Villegas, Tommaso Gili, Guido Caldarelli, Andrea Gabrielli

The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is particularly challenging due to correlations between intertwined scales. To date, the explorations are based on hidden geometries hypotheses. Here, we propose a Laplacian RG diffusion-based picture in complex networks, defining both the Kadanoff supernodes' concept, the momentum space procedure, \emph{\'a la Wilson}, and applying this RG scheme to real networks in a natural and parsimonious way.

Similar papers 1

96% Match

Guido Caldarelli, Andrea Gabrielli, ... , Villegas Pablo

The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification in a relatively small set of universality classes. RG is the most powerful tool for investigating organizational scales within dynamic systems. However, the application of RG techniques to complex networks has presented significant challenges, primarily due to the intricate i...

February 14, 2023

91% Match

Matheus de C. Loures, Alan Albert Piovesana, José Antônio Brum

Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify these systems is by creating miniaturized versions of the networks that keep their main properties. A convenient tool that applies that strategy is the renormalization group (RG), a methodology used in statistical physics to change the scales ...

November 17, 2008

91% Match

Filippo Radicchi, Alain Barrat, ... , Ramasco Jose J.

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw ...

January 20, 2024

91% Match

Marco Nurisso, Marta Morandini, Maxime Lucas, Francesco Vaccarino, ... , Petri Giovanni

We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based on diffusion dynamics was recently introduced for complex networks with dyadic interactions. Despite mounting evidence of the importance of polyadic interactions, we still lack a general RG scheme for higher-order networks. Our approach uses...

September 10, 2016

90% Match

Masamichi Sato

We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to build our original framework to infer the properties of biological networks, and the basis work to see its effectiveness to actual complex systems.

90% Match

Sungwon Jung, Sang Hoon Lee, Jaeyoon Cho

While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than resorting to handling the bare structure of a network, we overlay it with a readily renormalizable physical model, which reflects real-world scenarios with a broad generality. From the renormalization of the overlying system, we extract a rigorous ...

August 1, 2008

90% Match

Kento Ichikawa, Masato Uchida, ... , Oie Yuji

Nowadays, scaling methods for general large-scale complex networks have been developed. We proposed a new scaling scheme called "two-site scaling". This scheme was applied iteratively to various networks, and we observed how the degree distribution of the network changes by two-site scaling. In particular, networks constructed by the BA algorithm behave differently from the networks observed in the nature. In addition, an iterative scaling scheme can define a new renormalizin...

March 19, 2024

89% Match

der Kolk Jasper van, M. Ángeles Serrano, Marián Boguñá

The Renormalization Group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric space, is one of the foundational approaches. However, the current methods assume that the geometric coupling is strong, neglecting weak coupling in many real networks. This paper extends renormalization to weak geometric coupling, showing ...

September 26, 2009

89% Match

Hernán D. Rozenfeld, Chaoming Song, Hernán A. Makse

We show that renormalization group (RG) theory applied to complex networks are useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world/fractal transition by finding (i) a trivial stable fixed point of a complete graph, (ii) a non-trivial point of a pure fractal topology that is stable or unstable according to the amount of long-range links in the network, and (iii) another stable point of a f...

February 14, 2022

89% Match

Pablo Villegas, Andrea Gabrielli, Francesca Santucci, ... , Gili Tommaso

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information p...