Constructing and sampling directed graphs with given degree sequences
TLDR
This work presents an algorithm that can directly construct all possible realizations of a given bi-degree sequence by simple digraphs and provides their weight, which can then be used to compute statistical averages of network observables as if they were obtained from uniformly distributed sampling or from any other chosen distribution.Abstract:
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of simple labeled graphs with a given degree sequence is typically very large even for short sequences, sampling methods are needed for statistical studies. Currently, there are two main classes of methods that generate samples. One of the existing methods first generates a restricted class of graphs and then uses a Markov chain Monte-Carlo algorithm based on edge swaps to generate other realizations. As the mixing time of this process is still unknown, the independence of the samples is not well controlled. The other class of methods is based on the configuration model that may lead to unacceptably many sample rejections due to self-loops and multiple edges. Here we present an algorithm that can directly construct all possible realizations of a given bi-degree sequence by simple digraphs. Our method is rejection-free, guarantees the independence of the constructed samples and provides their weight. The weights can then be used to compute statistical averages of network observables as if they were obtained from uniformly distributed sampling or from any other chosen distribution.read more
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The structure and dynamics of multilayer networks
Stefano Boccaletti,Ginestra Bianconi,Regino Criado,Regino Criado,C.I. del Genio,Jesús Gómez-Gardeñes,Miguel Romance,Miguel Romance,Irene Sendiña-Nadal,Irene Sendiña-Nadal,Zhen Wang,Massimiliano Zanin +11 more
TL;DR: This work offers a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.
Journal ArticleDOI
The structure and dynamics of multilayer networks
Stefano Boccaletti,Ginestra Bianconi,Regino Criado,Regino Criado,C.I. del Genio,Jesús Gómez-Gardeñes,Miguel Romance,Miguel Romance,Irene Sendiña-Nadal,Irene Sendiña-Nadal,Zhen Wang,Massimiliano Zanin +11 more
TL;DR: In this article, a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.
Journal ArticleDOI
The statistical physics of real-world networks
Giulio Cimini,Giulio Cimini,Tiziano Squartini,Fabio Saracco,Diego Garlaschelli,Diego Garlaschelli,Andrea Gabrielli,Andrea Gabrielli,Guido Caldarelli +8 more
TL;DR: This Review describes advances in the statistical physics of complex networks and provides a reference for the state of the art in theoretical network modelling and applications to real-world systems for pattern detection and network reconstruction.
Journal ArticleDOI
Emergence of bimodality in controlling complex networks
Tao Jia,Yang-Yu Liu,Yang-Yu Liu,Endre Csóka,Márton Pósfai,Márton Pósfai,Márton Pósfai,Jean-Jacques E. Slotine,Albert-László Barabási +8 more
TL;DR: An analytical framework is developed to identify the category of each node in a network, leading to the discovery of two distinct control modes in complex systems: centralized versus distributed control.
Journal ArticleDOI
Quantifying randomness in real networks.
Chiara Orsini,Marija Mitrović Dankulov,Marija Mitrović Dankulov,Pol Colomer-de-Simón,Almerima Jamakovic,Priya Mahadevan,Amin Vahdat,Kevin E. Bassler,Zoltán Toroczkai,Marián Boguñá,Guido Caldarelli,Santo Fortunato,Dmitri Krioukov,Dmitri Krioukov +13 more
TL;DR: This work considers six real networks and finds that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network.
References
More filters
Book
Social Network Analysis: Methods and Applications
TL;DR: This paper presents mathematical representation of social networks in the social and behavioral sciences through the lens of Dyadic and Triadic Interaction Models, which describes the relationships between actor and group measures and the structure of networks.
Journal ArticleDOI
Social Network Analysis: Methods and Applications.
TL;DR: This work characterizes networked structures in terms of nodes (individual actors, people, or things within the network) and the ties, edges, or links that connect them.
Book
Networks: An Introduction
TL;DR: This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Journal ArticleDOI
Complex networks: Structure and dynamics
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
Journal ArticleDOI
Network Motifs: Simple Building Blocks of Complex Networks
TL;DR: Network motifs, patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks, are defined and may define universal classes of networks.