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Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…

Physics and Society · Physics 2025-07-22 Nicholas W. Landry , Jean-Gabriel Young , Nicole Eikmeier

Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of…

Physics and Society · Physics 2010-09-16 Yong-Yeol Ahn , James P. Bagrow , Sune Lehmann

A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…

Physics and Society · Physics 2018-04-18 María Pereda , Ernesto Estrada

Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…

Methodology · Statistics 2020-11-04 Marco Scutari

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 the human brain remains the Holy Grail in biomedical science, and arguably in all of the sciences. Our brains represent the most complex systems in the world (and some contend the universe) comprising nearly one hundred…

Quantitative Methods · Quantitative Biology 2016-02-03 Sean L. Simpson , Paul J. Laurienti

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,…

One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex…

Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different…

Formal Languages and Automata Theory · Computer Science 2011-08-18 Federico Buti , Massimo Callisto De Donato , Flavio Corradini , Emanuela Merelli , Luca Tesei

Complex biological networks are fundamental to biomedical science, capturing interactions among molecules, cells, genes, and tissues. Deciphering these networks is critical for understanding health and disease, yet their scale and…

Machine Learning · Computer Science 2025-12-09 Sakib Mostafa , Lei Xing , Md. Tauhidul Islam

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…

A common feature of biological networks is the geometric property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks, show self-similar…

Molecular Networks · Quantitative Biology 2012-03-09 Simon DeDeo , David C. Krakauer

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…

Physics and Society · Physics 2010-07-19 Dirk Helbing

The article presents several approaches to the blockmodeling of multilevel network data. Multilevel network data consist of networks that are measured on at least two levels (e.g. between organizations and people) and information on ties…

Methodology · Statistics 2014-05-26 Aleš Žiberna

Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…

Molecular Networks · Quantitative Biology 2013-05-29 Johannes Norrell , Joshua E. S. Socolar

Complex systems are often characterized by distinct types of interactions between the same entities. These can be described as a multilayer network where each layer represents one type of interaction. These layers may be interdependent in…

Social and Information Networks · Computer Science 2018-08-21 Caterina De Bacco , Eleanor A. Power , Daniel B. Larremore , Cristopher Moore

Many animals live in societies where individuals frequently interact socially with each other. The social structures of these systems can be studied in depth by means of network analysis. A large number of studies on animal social networks…

Populations and Evolution · Quantitative Biology 2021-02-22 Josefine Bohr Brask , Samuel Ellis , Darren P Croft

This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly…

Social and Information Networks · Computer Science 2015-03-24 Biswajit Saha , Amitabha Mandal , Soumendu Bikas Tripathy , Debaprasad Mukherjee

Many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers, with links and nodes of qualitatively different types. While during the past few years…