Networks: An Introduction

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Networks: An Introduction

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Networks: An Introduction

25 Mar 2010-

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.

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Abstract: The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. 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. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.

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Journal Article•DOI•

Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion

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Jonathan D. Power¹, Kelly Anne Barnes¹, Abraham Z. Snyder¹, Bradley L. Schlaggar, Steven E. Petersen - Show less +1 more•Institutions (1)

Washington University in St. Louis¹

01 Feb 2012-NeuroImage

TL;DR: The results suggest the need for greater care in dealing with subject motion, and the need to critically revisit previous rs-fcMRI work that may not have adequately controlled for effects of transient subject movements.

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6,411 citations

Cites background from "Networks: An Introduction"

...Normalizedmutual information is ameasure of shared information between probability distributions, and is a standard measure of the similarity of community assignments in elations in functional connectivity MRI networks arise from subject networks (Newman, 2010)....
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...networks (Newman, 2010)....
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Journal Article•DOI•

Catastrophic cascade of failures in interdependent networks

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Sergey V. Buldyrev¹, Sergey V. Buldyrev², Roni Parshani³, Gerald Paul², H. Eugene Stanley², Shlomo Havlin³ - Show less +2 more•Institutions (3)

Yeshiva University¹, Boston University², Bar-Ilan University³

15 Apr 2010-Nature

TL;DR: In this paper, the authors develop a framework for understanding the robustness of interacting networks subject to cascading failures and present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks.

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Abstract: Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures ('concurrent malfunction') is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

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3,651 citations

Journal Article•DOI•

Functional network organization of the human brain

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Jonathan D. Power¹, Alexander L. Cohen¹, Steven M. Nelson¹, Gagan S. Wig¹, Kelly Anne Barnes¹, Jessica A. Church¹, Alecia C. Vogel¹, Timothy O. Laumann¹, F.M. Miezin¹, Bradley L. Schlaggar¹, Steven E. Petersen - Show less +7 more•Institutions (1)

Washington University in St. Louis¹

17 Nov 2011-Neuron

TL;DR: In this article, the authors studied functional brain organization in healthy adults using resting state functional connectivity MRI and proposed two novel brain wide graphs, one of 264 putative functional areas, the other a modification of voxelwise networks that eliminates potentially artificial short-distance relationships.

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3,517 citations

Cites background or methods from "Networks: An Introduction"

...Many real-world networks have tie densities of a few percent or less (Newman, 2010), and the graph analytic techniques utilized here were developed upon such networks (Fortunato, 2010; Newman, 2010; Rosvall and Bergstrom, 2008)....
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...Because most graph theoretic techniques are developed (and are most meaningful) in sparse graphs (Newman, 2010), thresholds were applied to the graphs to eliminate weak ties (such that correlations under the threshold were ignored)....
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...…in graph theory includes quantifying hierarchy and substructure within a graph, identifying hubs and critical nodes, determining how easily traffic flows in different portions and at different scales of a network, and estimating the controllability of a system (Liu et al., 2011; Newman, 2010)....
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Journal Article•DOI•

Epidemic processes in complex networks

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Romualdo Pastor-Satorras¹, Claudio Castellano², Piet Van Mieghem³, Alessandro Vespignani⁴•Institutions (4)

Polytechnic University of Catalonia¹, Sapienza University of Rome², Delft University of Technology³, Northeastern University⁴

31 Aug 2015-Reviews of Modern Physics

TL;DR: A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear.

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Abstract: Complex networks arise in a wide range of biological and sociotechnical systems. Epidemic spreading is central to our understanding of dynamical processes in complex networks, and is of interest to physicists, mathematicians, epidemiologists, and computer and social scientists. This review presents the main results and paradigmatic models in infectious disease modeling and generalized social contagion processes.

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3,173 citations

Cites background from "Networks: An Introduction"

...…dynamic selforganization and are statistically heterogeneous—typical hallmarks of complex systems (Albert and Barabási, 2002; Baronchelli et al., 2013; Boccaletti et al., 2006; Caldarelli, 2007; Cohen and Havlin, 2010; Costa et al., 2007; Dorogovtsev and Mendes, 2002, 2003; Newman, 2010, 2003b)....
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...…network model has been subject to an impressive number of variations and extension aimed at considering more realistic growing dynamics, accommodate for different exponents of the degree distribution and other properties such as high clustering and tunable degree-degree correlations (Newman, 2010)....
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...Network science is burgeoning at the moment, and for more extensive accounts of this field we refer the readers to some of the recent reference textbook on the subject (Caldarelli, 2007; Dorogovtsev, 2010; Dorogovtsev and Mendes, 2003; Newman, 2010)....
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...At the core of all data-driven modeling approaches lies the structure of human interactions, mobility and contacts patterns that finds its best representation in the form of networks (Butts, 2009; Jackson, 2010; Newman, 2010; Vespignani, 2009, 2012)....
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Journal Article•DOI•

The structure and dynamics of multilayer networks

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Stefano Boccaletti, Ginestra Bianconi¹, Regino Criado², Regino Criado³, C.I. del Genio⁴, Jesús Gómez-Gardeñes⁵, Miguel Romance², Miguel Romance³, Irene Sendiña-Nadal², Irene Sendiña-Nadal³, Zhen Wang⁶, Massimiliano Zanin⁷ - Show less +8 more•Institutions (7)

Queen Mary University of London¹, Technical University of Madrid², King Juan Carlos University³, University of Warwick⁴, University of Zaragoza⁵, Hong Kong Baptist University⁶, Universidade Nova de Lisboa⁷

01 Nov 2014-Physics Reports

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.

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2,669 citations