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A plethora of networks is being collected in a growing number of fields, including disease transmission, international relations, social interactions, and others. As data streams continue to grow, the complexity associated with these highly…

Machine Learning · Statistics 2018-09-11 Daniele Durante , Nabanita Mukherjee , Rebecca C. Steorts

Community detection is a fascinating and rapidly evolving field, but when it comes to analyzing networks with multiple types of interactions, referred to as multilayer networks, there is still a lot of untapped potential. Despite the wide…

Social and Information Networks · Computer Science 2025-12-01 Randa Boukabene , Fatima Benbouzid Si Tayeb

A wide range of complex systems can be modeled as networks with corresponding constraints on the edges and nodes, which have been extensively studied in recent years. Nowadays, with the progress of information technology, systems that…

Physics and Society · Physics 2016-05-24 Han Zhang , Chang-Dong Wang , Jian-Huang Lai , Philip S. Yu

Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…

Disordered Systems and Neural Networks · Physics 2018-07-04 Guillermo García-Pérez , Marián Boguñá , M. Ángeles Serrano

Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A…

Physics and Society · Physics 2020-06-29 Andrea Santoro , Vincenzo Nicosia

The mental lexicon is a complex cognitive system representing information about the words/concepts that one knows. Decades of psychological experiments have shown that conceptual associations across multiple, interactive cognitive levels…

Computation and Language · Computer Science 2022-10-04 Massimo Stella , Salvatore Citraro , Giulio Rossetti , Daniele Marinazzo , Yoed N. Kenett , Michael S. Vitevitch

Antifragility is a property from which systems are able to resist stress and furthermore benefit from it. Even though antifragile dynamics is found in various real-world complex systems where multiple subsystems interact with each other,…

Adaptation and Self-Organizing Systems · Physics 2026-02-04 Hyobin Kim , Omar K. Pineda , Carlos Gershenson

The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer…

Physics and Society · Physics 2020-11-03 Xiangrong Wang , Alejandro Tejedor , Yi Wang , Yamir Moreno

Multi-layered social networks reflect complex relationships existing in modern interconnected IT systems. In such a network each pair of nodes may be linked by many edges that correspond to different communication or collaboration user…

Social and Information Networks · Computer Science 2012-10-19 Piotr Bródka , Krzysztof Skibicki , Przemysław Kazienko , Katarzyna Musiał

Multilayer networks offer a powerful framework for modeling complex systems across diverse domains, effectively capturing multiple types of connections and interdependent subsystems commonly found in real world scenarios. To analyze these…

Social and Information Networks · Computer Science 2026-02-20 Martin Guillemaud , Vera Dinkelacker , Mario Chavez

Understanding cooperation in social dilemmas requires models that capture the complexity of real-world interactions. While network frameworks have provided valuable insights to model the evolution of cooperation, they are unable to encode…

Physics and Society · Physics 2025-07-15 Onkar Sadekar , Andrea Civilini , Vito Latora , Federico Battiston

Networks (or graphs) are used to model the dyadic relations between entities in a complex system. In cases where there exists multiple relations between the entities, the complex system can be represented as a multilayer network, where the…

Social and Information Networks · Computer Science 2019-10-04 Abhishek Santra , Sanjukta Bhowmick , Sharma Chakravarthy

Multilayer networks provide a more advanced and comprehensive framework for modeling real-world systems compared to traditional single-layer and multiplex networks. Unlike single-layer models, multilayer networks have multiple interacting…

Optimization and Control · Mathematics 2025-02-26 Christian D. Rodríguez-Camargo , Andrés F. Urquijo-Rodríguez , Eduardo Mojica-Nava

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…

A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level,…

Physics and Society · Physics 2015-05-20 Xiu-Lian Xu , Yan-Qin Qu , Shan Guan , Yu-Mei Jiang , Da-Ren He

Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…

Adaptation and Self-Organizing Systems · Physics 2021-06-25 Rico Berner , Volker Mehrmann , Eckehard Schöll , Serhiy Yanchuk

Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…

Quantitative Methods · Quantitative Biology 2018-02-06 M. De Domenico

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

Disordered Systems and Neural Networks · Physics 2024-10-22 Blai Vidiella , Salva Duran-Nebreda , Sergi Valverde

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…

Physics and Society · Physics 2017-09-11 Kaj-Kolja Kleineberg , Marian Boguna , M. Angeles Serrano , Fragkiskos Papadopoulos