Barabasi

P. Deville, C. Song, N. Eagle, V. D. Blondel, A.-L. Barabasi, D. Wang

Scaling Identity Connects Human Mobility and Social Interactions

PNAS 113: 26, 7047-7052 (2016)

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Both our mobility and communication patterns obey spatial constraints: Most of the time, our trips or communications occur over a short distance, and occasionally, we take longer trips or call a friend who lives far away. These spatial dependencies, best described as power laws, play a consequential role in broad areas ranging from how an epidemic spreads to diffusion of ideas and information. Here we established the first formal link, to our knowledge, between mobility and communication patterns by deriving a scaling relationship connecting them. The uncovered scaling theory not only allows us to derive human movements from communication volumes, or vice versa, but it also documents a new degree of regularity that helps deepen our quantitative understanding of human behavior. Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality.
Barabasi

R. Sinatra, P. Deville, M. Szell, D. Wang, A.-L. Barabási

A century of physics

Nature Physics 11, 791-796 (2015)

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An analysis of Web of Science data spanning more than 100 years reveals the rapid growth andincreasing multidisciplinary of physics — as well its internal map of sub-disciplines.
Barabasi

L. Pappalardo, F. Simini, S. Rinzivillo, D. Pedreschi, F. Giannotti, A.-L. Barabási

Returners and explorers dichotomy in human mobility

Nature Communications 6:8166, 1-8 (2015)

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The availability of massive digital traces of human whereabouts has offered a series of novel insights on the quantitative patterns characterizing human mobility. In particular, numerous recent studies have lead to an unexpected consensus: the considerable variability in the characteristic travelled distance of individuals coexists with a high degree of predictability of their future locations. Here we shed light on this surprising coexistence by systematically investigating the impact of recurrent mobility on the characteristic distance travelled by individuals. Using both mobile phone and GPS data, we discover the existence of two distinct classes of individuals: returners and explorers. As existing models of human mobility cannot explain the existence of these two classes, we develop more realistic models able to capture the empirical findings. Finally, we show that returners and explorers play a distinct quantifiable role in spreading phenomena and that a correlation exists between their mobility patterns and social interactions.
Barabasi

B. Barzel, Y.-Y. Liu, A.-L. Barabási

Constructing minimal models for complex system dynamics

Nature Communications 6:7186, 1-8 (2015)

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One of the strengths of statistical physics is the ability to reduce macroscopic observations into microscopic models, offering a mechanistic description of a system’s dynamics. This paradigm, rooted in Boltzmann’s gas theory, has found applications from magnetic phenomena to subcellular processes and epidemic spreading. Yet, each of these advances were the result of decades of meticulous model building and validation, which are impossible to replicate in most complex biological, social or technological systems that lack accurate microscopic models. Here we develop a method to infer the microscopic dynamics of a complex system from observations of its response to external perturbations, allowing us to construct the most general class of nonlinear pairwise dynamics that are guaranteed to recover the observed behavior. The result, which we test against both numerical and empirical data, is an effective dynamic model that can predict the system’s behavior and provide crucial insights into its inner workings.
Barabasi

S. D. Ghiassian, J. Menche, A.-L. Barabási

A DIseAse MOdule Detection (DIAMOnD) Algorithm Derived from a Systematic Analysis of Connectivity Patterns of Disease Proteins in the Human Interactome

PLOS Computational Biology pcbi.1004120, 1-21 (2015)

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The observation that disease associated proteins often interact with each other has fueled the development of network-based approaches to elucidate the molecular mechanisms of human disease. Such approaches build on the assumption that protein interaction networks can be viewed as maps in which diseases can be identified with localized perturbation within a certain neighborhood. The identification of these neighborhoods, or disease modules, is therefore a prerequisite of a detailed investigation of a particular pathophenotype. While numerous heuristic methods exist that successfully pinpoint disease associated modules, the basic underlying connectivity patterns remain largely unexplored. In this work we aim to fill this gap by analyzing the network properties of a comprehensive corpus of 70 complex diseases. We find that disease associated proteins do not reside within locally dense communities and instead identify connectivity significance as the most predictive quantity. This quantity inspires the design of a novel Disease Module Detection (DIAMOnD) algorithm to identify the full disease module around a set of known disease proteins. We study the performance of the algorithm using well-controlled synthetic data and systematically validate the identified neighborhoods for a large corpus of diseases.
Barabasi

Jianxi Gao, Y.-Y.Liu, R. M. D'Souza, A.-L. Barabási

Target control of complex networks

Nature Communications 5:5415, 1-7 (2014)

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Controlling large natural and technological networks is an outstanding challenge. It is typically neither feasible nor necessary to control the entire network, prompting us to explore target control: the efficient control of a preselected subset of nodes. We show that the structural controllability approach used for full control overestimates the minimum number of driver nodes needed for target control. Here we develop an alternate ‘k-walk’ theory for directed tree networks, and we rigorously prove that one node can control a set of target nodes if the path length to each target node is unique. For more general cases, we develop a greedy algorithm to approximate the minimum set of driver nodes sufficient for target control. We find that degree heterogeneous networks are target controllable with higher efficiency than homogeneous networks and that the structure of many real-world networks are suitable for efficient target control.
Barabasi

H.-W. Shen, A.-L. Barabasi

Collective credit allocation in science

Proceedings of the National Academy of Sciences 10.1073/pnas.1401992111, 1-6 (2014)

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Collaboration among researchers is an essential component of the modern scientific enterprise, playing a particularly important role in multidisciplinary research. However, we _continue to wrestle with allocating credit to the coauthors of publications with multiple authors, because the relative contribution of each author is difficult to determine. At the same time, the scientific community runs an informal field-dependent credit allocation process that assigns credit in a collective fashion to each work. Here we develop a credit allocation algorithm that captures the coauthors’ contribution to a publication as perceived by the scientific community, reproducing the informal collective credit allocation of science. We validate the method by identifying the authors of Nobel-winning papers that are credited for the discovery, independent of their positions in the author list. The method can also compare the relative impact of researchers working in the same field, even if they did not publish together. The ability to accurately measure the relative credit of researchers could affect many aspects of credit allocation in science, potentially impacting hiring, funding, and promotion decisions.
Barabasi

M. Schich, C. Song, Y. Y. Ahn, A. Mirsky, M. Martino, A.-L. Barabási, D. Helbing

A network framework of cultural history

Science 345, 558-562 (2014)

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The emergent processes driving cultural history are a product of complex interactions among large numbers of individuals, determined by difficult-to-quantify historical conditions. To characterize these processes, we have reconstructed aggregate intellectual mobility over two millennia through the birth and death locations of more than 150,000 notable individuals. The tools of network and complexity theory were then used to identify characteristic statistical patterns and determine the cultural and historical relevance of deviations. The resulting network of locations provides a macroscopic perspective of cultural history, which helps us to retrace cultural narratives of Europe and North America using large-scale visualization and quantitative dynamical tools and to derive historical trends of cultural centers beyond the scope of specific events or narrow time intervals. Watch the Nature Video "Charting Culture" here: https://www.youtube.com/watch?v=4gIhRkCcD4U
Barabasi

H. Shen, D. Wang, C. Song, A.-L. Barabási

Modeling and predicting popularity dynamics via reinforced poisson processes

Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence , 291-297 (2014)

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An ability to predict the popularity dynamics of individual items within a complex evolving system has important implications in an array of areas. Here we propose a generative probabilistic framework using a reinforced Poisson process to explicitly model the process through which individual items gain their popularity. This model distinguishes itself from existing models via its capability of modeling the arrival process of popularity and its remarkable power at predicting the popularity of individual items. It possesses the flexibility of applying Bayesian treatment to further improve the predictive power using a conjugate prior. Extensive experiments on a longitudinal citation dataset demonstrate that this model consistently outperforms existing popularity prediction methods.
Barabasi

X. Z. Zhou, J. Menche, A.-L. Barabási, A. Sharma

Human symptoms–disease network

Nature Communications 5:4212, 1-10 (2014)

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In the post-genomic era, the elucidation of the relationship between the molecular origins of diseases and their resulting phenotypes is a crucial task for medical research. Here, we use a large-scale biomedical literature database to construct a symptom-based human disease network and investigate the connection between clinical manifestations of diseases and their underlying molecular interactions. We find that the symptom-based similarity of two diseases correlates strongly with the number of shared genetic associations and the extent to which their associated proteins interact. Moreover, the diversity of the clinical manifestations of a disease can be related to the connectivity patterns of the underlying protein interaction network. The comprehensive, high-quality map of disease–symptom relations can further be used as a resource helping to address important questions in the field of systems medicine, for example, the identification of unexpected associations between diseases, disease etiology research or drug design.
Barabasi

P. Deville, D. Wang, R. Sinatra, C. Song, V. Blondel, A.-L. Barabási

Career on the move: Geography, stratification, and scientific impact

Scientific Reports 4, 1-7 (2014)

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Changing institutions is an integral part of an academic life. Yet little is known about the mobility patterns of scientists at an institutional level and how these career choices affect scientific outcomes. Here, we examine over 420,000 papers, to track the affiliation information of individual scientists, allowing us to reconstruct their career trajectories over decades. We find that career movements are not only temporally and spatially localized, but also characterized by a high degree of stratification in institutional ranking. When cross-group movement occurs, we find that while going from elite to lower-rank institutions on average associates with modest decrease in scientific performance, transitioning into elite institutions does not result in subsequent performance gain. These results offer empirical evidence on institutional level career choices and movements and have potential implications for science policy.
Barabasi

L. Gao, C. Song, Z. Gao, A.-L. Barabasi, J. P. Bagrow, D. Wang

Quantifying information flow during emergencies

Scientific Reports 4, 1-6 (2014)

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Recent advances on human dynamics have focused on the normal patterns of human activities, with the quantitative understanding of human behavior under extreme events remaining a crucial missing chapter. This has a wide array of potential applications, ranging from emergency response and detection to traffic control and management. Previous studies have shown that human communications are both temporally and spatially localized following the onset of emergencies, indicating that social propagation is a primary means to propagate situational awareness. We study real anomalous events using country-wide mobile phone data, finding that information flow during emergencies is dominated by repeated communications. We further demonstrate that the observed communication patterns cannot be explained by inherent reciprocity in social networks, and are universal across different demographics.
Barabasi

G. Ghoshal, L. Chi, A.-L. Barabási

Uncovering the role of elementary processes in network evolution

Scientifc Reports 3, 1-8 (2013)

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The growth and evolution of networks has elicited considerable interest from the scientific community and a number of mechanistic models have been proposed to explain their observed degree distributions. Various microscopic processes have been incorporated in these models, among them, node and edge addition, vertex fitness and the deletion of nodes and edges. The existing models, however, focus on specific combinations of these processes and parameterize them in a way that makes it difficult to elucidate the role of the individual elementary mechanisms. We therefore formulated and solved a model that incorporates the minimal processes governing network evolution. Some contribute to growth such as the formation of connections between existing pair of vertices, while others capture deletion; the removal of a node with its corresponding edges, or the removal of an edge between a pair of vertices. We distinguish between these elementary mechanisms, identifying their specific role on network evolution.
Barabasi

D. Wang, C. Song, A.-L. Barabási

Quantifying Long-Term Scientific Impact

Science 342, 127-131 (2013)

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The lack of predictability of citation-based measures frequently used to gauge impact, from impact factors to short-term citations, raises a fundamental question: Is there long-term predictability in citation patterns? Here, we derive a mechanistic model for the citation dynamics of individual papers, allowing us to collapse the citation histories of papers from different journals and disciplines into a single curve, indicating that all papers tend to follow the same universal temporal pattern. The observed patterns not only help us uncover basic mechanisms that govern scientific impact but also offer reliable measures of influence that may have potential policy implications.
Barabasi

B. Barzel, A.-L. Barabási

Universality in network dynamics

Nature Physics 9, 673-681 (2013)

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Despite significant advances in characterizing the structural properties of complex networks, a mathematical framework that uncovers the universal properties of the interplay between the topology and the dynamics of complex systems continues to elude us. Here we develop a self-consistent theory of dynamical perturbations in complex systems, allowing us to systematically separate the contribution of the network topology and dynamics. The formalism covers a broad range of steady-state dynamical processes and offers testable predictions regarding the system’s response to perturbations and the development of correlations. It predicts several distinct universality classes whose characteristics can be derived directly from the continuum equation governing the system’s dynamics and which are validated on several canonical network-based dynamical systems, from biochemical dynamics to epidemic spreading. Finally, we collect experimental data pertaining to social and biological systems, demonstrating that we can accurately uncover their universality class even in the absence of an appropriate continuum theory that governs the system’s dynamics.
Barabasi

T. Jia, A.-L. Barabási

Control capacity and a random sampling method in exploring controllability of complex networks

Scientific Reports 3:2354, 1-6 (2013)

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Controlling complex systems is a fundamental challenge of network science. Recent advances indicate that control over the system can be achieved through a minimum driver node set (MDS). The existence of multiple MDS's suggests that nodes do not participate in control equally, prompting us to quantify their participations. Here we introduce control capacity quantifying the likelihood that a node is a driver node. To efficiently measure this quantity, we develop a random sampling algorithm. This algorithm not only provides a statistical estimate of the control capacity, but also bridges the gap between multiple microscopic control configurations and macroscopic properties of the network under control. We demonstrate that the possibility of being a driver node decreases with a node's in-degree and is independent of its out-degree. Given the inherent multiplicity of MDS's, our findings offer tools to explore control in various complex systems.
Barabasi

B. Barzel, A.-L. Barabási

Network link prediction by global silencing of indirect correlations

Nature Biotechnology 31: Num 8, 1-8 (2013)

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Predictions of physical and functional links between cellular components are often based on correlations between experimental measurements, such as gene expression. However, correlations are affected by both direct and indirect paths, confounding our ability to identify true pairwise interactions. Here we exploit the fundamental properties of dynamical correlations in networks to develop a method to silence indirect effects. The method receives as input the observed correlations between node pairs and uses a matrix transformation to turn the correlation matrix into a highly discriminative silenced matrix, which enhances only the terms associated with direct causal links. Against empirical data for Escherichia coli regulatory interactions, the method enhanced the discriminative power of the correlations by twofold, yielding >50% predictive improvement over traditional correlation measures and 6% over mutual information. Overall this silencing method will help translate the abundant correlation data into insights about a system's interactions, with applications ranging from link prediction to inferring the dynamical mechanisms governing biological networks.
Barabasi

T. Jia, Y.-Y. Liu, E. Csóka, M. Pósfai, J.-J. Slotine, A.-L. Barabási

Emergence of bimodality in controlling complex networks

Nature Communications 4:2002, 1-6 (2013)

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Our ability to control complex systems is a fundamental challenge of contemporary science. Recently introduced tools to identify the driver nodes, nodes through which we can achieve full control, predict the existence of multiple control configurations, prompting us to classify each node in a network based on their role in control. Accordingly a node is critical, intermittent or redundant if it acts as a driver node in all, some or none of the control configurations. Here we develop an analytical framework to identify the category of each node, leading to the discovery of two distinct control modes in complex systems: centralized versus distributed control. We predict the control mode for an arbitrary network and show that one can alter it through small structural perturbations. The uncovered bimodality has implications from network security to organizational research and offers new insights into the dynamics and control of complex systems.
Barabasi

M. Pósfai, Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási

Effect of correlations on network controllability

Scientific Reports 3:1067, 1-7 (2013)

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A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but the symmetries of the underlying matching problem can produce linear, quadratic or no dependence on degree correlation coefficients, depending on the nature of the underlying correlations. The results are supported by numerical simulations and help narrow the observed gap between the predicted and the observed number of driver nodes in real networks.
Barabasi

Y.-Y. Liu, J.-J. Slotine, A.-L. Barabasi

Control centrality and hierarchical structure in complex networks

PLoS One 7, e44459 (2012

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We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network’s degree distribution. We show that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
Barabasi

N. Blumm, G. Ghoshal, Z. Forro, M. Schich, G. Bianconi, J.-P. Bouchard, A.-L. Barabasi

Dynamics of ranking processes in complex systems

Physical Review Letters 109, 128701:1-5 (2012)

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The world is addicted to ranking: everything, from the reputation of scientists, journals, and universities to purchasing decisions is driven by measured or perceived differences between them. Here, we analyze empirical data capturing real time ranking in a number of systems, helping to identify the universal characteristics of ranking dynamics. We develop a continuum theory that not only predicts the stability of the ranking process, but shows that a noise-induced phase transition is at the heart of the observed differences in ranking regimes. The key parameters of the continuum theory can be explicitly measured from data, allowing us to predict and experimentally document the existence of three phases that govern ranking stability.
Barabasi

Albert-László Barabási

Network science: Luck or reason

Nature 489, 1-2 (2012)

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The concept of preferential attachment is behind the hubs and power laws seen in many networks. New results fuel an old debate about its origin, and beg the question of whether it is based on randomness or optimization.
Barabasi

V. Palchykov, K. Kaski, J. Kertesz, A.-L. Barabási, R. Dunbar

Sex differences in intimate relationships

Scientific Reports 2:370, 105 (2012)

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Social networks based on dyadic relationships are fundamentally important for understanding of human sociality. However, we have little understanding of the dynamics of close relationships and how these change over time. Evolutionary theory suggests that, even in monogamous mating systems, the pattern of investment in close relationships should vary across the lifespan when post-weaning investment plays an important role in maximizing fitness. Mobile phone data sets provide a unique window into the structure and dynamics of relationships. We here use data from a large mobile phone dataset to demonstrate striking sex differences in the gender-bias of preferred relationships that reflect the way the reproductive investment strategies of both sexes change across the lifespan, i.e. women’s shifting patterns of investment in reproduction and parental care. These results suggest that human social strategies may have more complex dynamics than previously assumed and a life-history perspective is crucial for understanding them.
Barabasi

F. Simini, M. González, A. Maritan, A.-L. Barabási

A universal model for mobility and migration patterns

Nature 484, 96-100 (2012)

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Introduced in its contemporary form in 1946, but with roots that go back to the eighteenth century, the gravity law is the prevailing framework with which to predict population movement, cargo shipping volume and inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes.
Barabasi

Y.-Y. Ahn, S. E. Ahnert, J. P. Bagrow, A.-L. Barabási

Flavor network and the principles of food pairing

Scientific Reports 196, (2011)

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The cultural diversity of culinary practice, as illustrated by the variety of regional cuisines, raises the question of whether there are any general patterns that determine the ingredient combinations used in food today or principles that transcend individual tastes and recipes. We introduce a flavor network that captures the flavor compounds shared by culinary ingredients. Western cuisines show a tendency to use ingredient pairs that share many flavor compounds, supporting the so-called food pairing hypothesis. By contrast, East Asian cuisines tend to avoid compound sharing ingredients. Given the increasing availability of information on food preparation, our data-driven investigation opens new avenues towards a systematic understanding of culinary practice.
Barabasi

D. Wang, D. Pedreschi, C. Song, F. Giannotti, A.-L. Barabasi

Human Mobility, Social Ties, and Link Prediction

ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD) , (2011)

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Our understanding of how individual mobility patterns shape and impact the social network is limited, but is essential for a deeper understanding of network dynamics and evolution. This question is largely unexplored, partly due to the difficulty in obtaining large-scale society-wide data that simultaneously capture the dynamical information on individual movements and social interactions. Here we address this challenge for the first time by tracking the trajectories and communication records of 6 Million mobile phone users. We find that the similarity between two individuals' movements strongly correlates with their proximity in the social network. We further investigate how the predictive power hidden in such correlations can be exploited to address a challenging problem: which new links will develop in a social network. We show that mobility measures alone yield surprising predictive power, comparable to traditional network-based measures. Furthermore, the prediction accuracy can be significantly improved by learning a supervised classifier based on combined mobility and network measures. We believe our findings on the interplay of mobility patterns and social ties offer new perspectives on not only link prediction but also network dynamics.
Barabasi

Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási

Few inputs can reprogram biological networks (reply by Liu et al.)

Nature 473, 167-173 (2011)

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Reply to Franz-Josef Muller and Andreas Schuppert (Nature 478, Pg. E4, Oct. 2011)
Barabasi

Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási

Controllability of complex networks

Nature 473, 167-173 (2011)

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The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.
Barabasi

J. P. Onnela, S. Arbesman, M. C. Gonzalez, A.-L. Barabasi, N. A. Christakis

Geographic Constraints on Social Network Groups

PLoS One 6:4, 1-7 (2011)

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Social groups are fundamental building blocks of human societies. While our social interactions have always been constrained by geography, it has been impossible, due to practical difficulties, to evaluate the nature of this restriction on social group structure. We construct a social network of individuals whose most frequent geographical locations are also known. We also classify the individuals into groups according to a community detection algorithm. We study the variation of geographical span for social groups of varying sizes, and explore the relationship between topological positions and geographic positions of their members. We find that small social groups are geographically very tight, but become much more clumped when the group size exceeds about 30 members. Also, we find no correlation between the topological positions and geographic positions of individuals within network communities. These results suggest that spreading processes face distinct structural and spatial constraints.
Barabasi

J. P. Bagrow, D. Wang, A.-L. Barabasi

Collective response of human populations to large-scale emergencies

PLoS One 6:3, 1-8 (2011)

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Despite recent advances in uncovering the quantitative features of stationary human activity patterns, many applications,from pandemic prediction to emergency response, require an understanding of how these patterns change when thepopulation encounters unfamiliar conditions. To explore societal response to external perturbations we identified real-timechanges in communication and mobility patterns in the vicinity of eight emergencies, such as bomb attacks andearthquakes, comparing these with eight non-emergencies, like concerts and sporting events. We find that communicationspikes accompanying emergencies are both spatially and temporally localized, but information about emergencies spreadsglobally, resulting in communication avalanches that engage in a significant manner the social network of eyewitnesses.These results offer a quantitative view of behavioral changes in human activity under extreme conditions, with potentiallong-term impact on emergency detection and response.
Barabasi

C. Song, T. Koren, P. Wang, A.-L. Barabási

Modelling the scaling properties of human mobility

Nature Physics 7, 713- (2010)

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Individual human trajectories are characterized by fat-tailed distributions of jump sizes and waiting times, suggesting the relevance of continuous-time random-walk (CTRW) models for human mobility. However, human traces are barely random. Given the importance of human mobility, from epidemic modelling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile-phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model accounts for the empirically observed scaling laws, but also allows us to analytically predict most of the pertinent scaling exponents.
Barabasi

C. Song, Z. Qu, N. Blumm, A.-L. Barabási

Limits of Predictability in Human Mobility

Science 327, 1018-1021 (2010)

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A range of applications, from predicting the spread of human and electronic viruses to city planning and resource management in mobile communications, depend on our ability to foresee the whereabouts and mobility of individuals, raising a fundamental question: To what degree is human behavior predictable? Here we explore the limits of predictability in human dynamics by studying the mobility patterns of anonymized mobile phone users. By measuring the entropy of each individual’s trajectory, we find a 93% potential predictability in user mobility across the whole user base. Despite the significant differences in the travel patterns, we find a remarkable lack of variability in predictability, which is largely independent of the distance users cover on a regular basis.
Barabasi

D. A. Davis, N. V. Chawla, N. A. Christakis, A.-L. Barabasi

Time to CARE: a collaborative engine for practical disease prediction

Data Mining and Knowledge Discovery 30:3, 388-41 (2009)

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The monumental cost of health care, especially for chronic disease treatment, is quickly becoming unmanageable. This crisis has motivated the drive towards preventative medicine, where the primary concern is recognizing disease risk and taking action at the earliest signs. However, universal testing is neither time nor cost efficient. We propose CARE, a Collaborative Assessment and Recommendation Engine, which relies only on patient’s medical history using ICD-9-CM codes in order to predict future disease risks. CARE uses collaborative filtering methods to predict each patient’s greatest disease risks based on their own medical history and that of similar patients. We also describe an Iterative version, ICARE, which incorporates ensemble concepts for improved performance. Also, we apply time-sensitive modifications which make the CARE framework practical for realistic long-term use. These novel systems require no specialized information and provide predictions for medical conditions of all kinds in a single run. We present experimental results on a larg Medicare dataset, demonstrating that CARE and ICARE perform well at capturing future disease risks.
Barabasi

A.-L. Barabási

Scale-Free Networks: A Decade and Beyond

Science 325, 412-413 (2009)

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For decades, we tacitly assumed that the components of such complex systems as the cell, the society, or the Internet are randomly wired together. In the past decade, an avalanche of research has shown that many real networks, independent of their age, function, and scope, converge to similar architectures, a universality that allowed researchers from different disciplines to embrace network theory as a common paradigm. The decade-old discovery of scale-free networks was one of those events that had helped catalyze the emergence of network science, a new research field with its distinct set of challenges and accomplishments.
Barabasi

P. Wang, M. Gonzalez, C. A. Hidalgo, A.-L. Barabási

Understanding the spreading patterns of mobile phone viruses

Science 324, 1071-1076 (2009)

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We modeled the mobility of mobile phone users in order to study the fundamental spreading patterns that characterize a mobile virus outbreak. We find that although Bluetooth viruses can reach all susceptible handsets with time, they spread slowly because of human mobility, offering ample opportunities to deploy antiviral software. In contrast, viruses using multimedia messaging services could infect all users in hours, but currently a phase transition on the underlying call graph limits them to only a small fraction of the susceptible users. These results explain the lack of a major mobile virus breakout so far and predict that once a mobile operating system’s market share reaches the phase transition point, viruses will pose a serious threat to mobile communications.
Barabasi

C. A. Hidalgo, N. Blumm, A.-L. Barabási, N. A. Christakis

A dynamic network approach for the study of human phenotypes

PLoS Computational Biology 5:4, 1-11 (2009)

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The use of networks to integrate different genetic, proteomic, and metabolic datasets has been proposed as a viable path toward elucidating the origins of specific diseases. Here we introduce a new phenotypic database summarizing correlations obtained from the disease history of more than 30 million patients in a Phenotypic Disease Network (PDN). We present evidence that the structure of the PDN is relevant to the understanding of illness progression by showing that (1) patients develop diseases close in the network to those they already have; (2) the progression of disease along the links of the network is different for patients of different genders and ethnicities; (3) patients diagnosed with diseases which are more highly connected in the PDN tend to die sooner than those affected by less connected diseases; and (4) diseases that tend to be preceded by others in the PDN tend to be more connected than diseases that precede other illnesses, and are associated with higher degrees of mortality. Our findings show that disease progression can be represented and studied using network methods, offering the potential to enhance our understanding of the origin and evolution of human diseases. The dataset introduced here, released concurrently with this publication, represents the largest relational phenotypic resource publicly available to the research community.
Barabasi

J. Park, D. S. Lee, N. A. Christakis, A.-L. Barabási

The impact of cellular networks on disease comorbidity

Molecular Systems Biology 5:262, 1-7 (2009)

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The impact of disease-causing defects is often not limited to the products of a mutated gene but, thanks to interactions between the molecular components, may also affect other cellular functions, resulting in potential comorbidity effects. By combining information on cellular interactions, disease--gene associations, and population-level disease patterns extracted from Medicare data, we find statistically significant correlations between the underlying structure of cellular networks and disease comorbidity patterns in the human population. Our results indicate that such a combination of population-level data and cellular network information could help build novel hypotheses about disease mechanisms.
Barabasi

D. Lazer, A. Pentland, L. Adamic, S. Aral, A.-L. Barabási, D. Brewer, N. Christakis, N. Contractor, J. Fowler, M. Gutmann, T. Jebara, G. King, M. Macy, D. Roy, M. Van Alstyne

Computation Social Science

Science 323, 721-724 (2009)

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We live life in the network. We check our e-mails regularly, make mobile phone calls from almost any location, swipe transit cards to use public transportation, and make purchases with credit cards. Our movements in public places may be captured by video cameras, and our medical records stored as digital files. We may post blog entries accessible to anyone, or maintain friendships through online social networks. Each of these transactions leaves digital traces that can be compiled into comprehensive pictures of both individual and group behavior, with the potential to transform our understanding of ourlives, organizations, and societies.
Barabasi

M. C. González, C. A. Hidalgo, A.-L. Barabási

Understanding individual human mobility patterns

Nature 453, 779-782 (2008)

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Despite their importance for urban planning, traffic forecasting and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited owing to the lack of tools to monitor the time-resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period. We find that, in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent-based modeling.
Barabasi

J. Candia, M. C. Gonzalez, P. Wang, T. Schoenharl, G. Madey, A.-L. Barabási

Uncovering individual and collective human dynamics from mobile phone records

Journal of Physics A: Mathematical and Theoretical 41, 1-11 (2008)

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Novel aspects of human dynamics and social interactions are investigated by means of mobile phone data. Using extensive phone records resolved in both time and space, we study the mean collective behavior at large scales and focus on the occurrence of anomalous events. We discuss how these spatiotemporal anomalies can be described using standard percolation theory tools. We also investigate patterns of calling activity at the individual level and show that the interevent time of consecutive calls is heavy-tailed. This finding, which has implications for dynamics of spreading phenomena in social networks, agrees with results previously reported on other human activities.
Barabasi

K.-L. Goh, A.-L. Barabási

Burstiness and memory in complex systems

Europhysics Letters 81, 48002 (2008)

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The dynamics of a wide range of real systems, from email patterns to earthquakes,display a bursty, intermittent nature, characterized by short timeframes of intense activity followed by long times of no or reduced activity. The understanding of the origin of such bursty patterns is hindered by the lack of tools to compare different systems using a common framework. Here we propose to characterize the bursty nature of real signals using orthogonal measures quantifying two distinct mechanisms leading to burstiness: the interevent time distribution and the memory. We find that while the burstiness of natural phenomena is rooted in both the interevent time distribution and memory, for human dynamics memory is weak, and the bursty character is due to the changes in the interevent time distribution. Finally, we show that current models lack in their ability to reproduce the activity pattern observed in real systems, opening up avenues for future work.
Barabasi

A.-L. Barabási

The architecture of complexity

IEEE Control Systems Magazine 27:4, 33-42 (2007)

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We are surrounded by complex systems, from cells made of thousands of molecules to society, a collection of billions of interacting individuals. These systems display signatures of order and self-organization. Understanding and quantifying this complexity is a grand challenge for science. Kinetic theory, developed at the end of the 19th century, shows that the measurable properties of gases, from pressure to temperature, can be reduced to the random motion of atoms and molecules. In the 1960s and 1970s, researchers developed systematic approaches to quantifying the transition from disorder to order in material systems such as magnets and liquids. Chaos theory dominated the quest to understand complex behavior in the 1980s with the message that unpredictable behavior can emerge from the nonlinear interactions of a few components. The 1990s was the decade of fractals, quantifying the geometry of patterns emerging in self-organized systems, from leaves to snowflakes.
Barabasi

J.-P. Onnela, J. Saramäki, J. Hyvönen, G. Szabó, M A. de Menezes, K. Kaski, A.-L. Barabási, J. Kertész

Analysis of a large-scale weighted network of one-to-one human communication

New Journal of Physics 9, 1-27 (2007)

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We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well as its topological assortativity and weighted assortativity, clustering and weighted clustering, together with correlations between these quantities.We give an account of motif intensity and coherence distributions and compare them to a randomized reference system.We also use the concept of link overlap to measure the number of common neighbours any two adjacent nodes have, which serves as a useful local measure for identifying the interconnectedness of communities. We report a positive correlation between the overlap and weight of a link, thus providing strong quantitative evidence for the weak ties hypothesis, a central concept in social network analysis. The percolation properties of the network are found to depend on the type and order of removed links, and they can help understand how the local structure of the network manifests itself at the global level.We hope that our results will contribute to modelling weighted large-scale social networks, and believe that the systematic approach followed here can be adopted to study other weighted networks.
Barabasi

A. Vazquez, B. Rácz, A. Lukács, A.-L. Barabási

Impact of non-Poissonian activity patterns on spreading processes

Physical Review Letters 98:15, 158702 (2007)

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Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time, following a Poisson process, a series of recent measurements indicates that the intercontact time distribution is heavy tailed, corresponding to a temporally inhomogeneous bursty contact process. Here we show that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Our predictions are in agreement with the detailed time resolved prevalence data of computer viruses, which, according to virus bulletins, show a decay time close to a year, in contrast with the 1 day decay predicted by the standard Poisson process based models.
Barabasi

G. Palla, A.-L. Barabási, T. Vicsek

Quantifying social group evolution

Nature 446:7136, 664-667 (2007)

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Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist for longer if they are capable of dynamically altering their membership, suggesting that an ability to change the group composition results in better adaptability. The behaviour of small groups displays the opposite tendency—the condition for stability is that their composition remains unchanged. We also show that knowledge of the time commitment of members to a given community can be used for estimating the community’s lifetime. These findings offer insight into the fundamental differences between the dynamics of small groups and large institutions.
Barabasi

M. C. Gonzalez, A.-L. Barabási

Complex networks - From data to models

Nature Physics 3, 224-225 (2007)

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Data on the movement of people becomes ever more detailed, but robust models explaining the observed patterns are still needed. Mapping the problem onto a 'network of networks' could be a promising approach.
Barabasi

Z. Dezso, E. Almaas, A. Lukacs, B. Racz, I. Szakadat, A.-L. Barabási

Dynamics of information access on the web

Physical Review E 73, 066132 (2006)

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While current studies on complex networks focus on systems that change relatively slowly in time, the structure of the most visited regions of the web is altered at the time scale from hours to days. Here we investigate the dynamics of visitation of a major news portal, representing the prototype for such a rapidly evolving network. The nodes of the network can be classified into stable nodes, which form the timeindependent skeleton of the portal, and news documents. The visitations of the two node classes are markedly different, the skeleton acquiring visits at a constant rate, while a news document’s visitation peaks after a few hours. We find that the visitation pattern of a news document decays as a power law, in contrast with the exponential prediction provided by simple models of site visitation. This is rooted in the inhomogeneous nature of the browsing pattern characterizing individual users: the time interval between consecutive visits by the same user to the site follows a power-law distribution, in contrast to the exponential expected for Poisson processes. We show that the exponent characterizing the individual user’s browsing patterns determines the power-law decay in a document’s visitation. Finally, our results document the fleeting quality of news and events: while fifteen minutes of fame is still an exaggeration in the online media, we find that access to most news items significantly decays after 36 hours of posting.
Barabasi

A. Vazquez, J.G. Oliveira, Z. Dezso, K.I. Goh, I. Kondor, A.-L. Barabási

Modeling bursts and heavy tails in human dynamics

Physical Review E 73, 036127 (2006)

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The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution Pww− with =3/2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by =1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display =1, the surface mail based communication belongs to the =3/2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.
Barabasi

J. G. Oliveira, A.-L. Barabási

Darwin and Einstein correspondence patterns

Nature 437, 1251 (2005)

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These scientists prioritized their replies to letters in the same way that people rate their e-mails today.
Barabasi

A.-L. Barabási

The origin of bursts and heavy tails in humans dynamics

Nature 435, 207 (2005)

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Here I show that the bursty nature of human behaviour is a consequence of a decision-based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times. In contrast, random or priority blind execution is well approximated by uniform inter-event statistics. These finding have important implications, ranging from resource management to service allocation, in both communications and retail.
Barabasi

Z. Eisler, J. Kertesz, S.-H. Yook, A.-L. Barabási

Multiscaling and non-universality in fluctuations of driven complex systems

Europhysics Letters 69, 664-670 (2005)

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For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the timedependent activity of a large number of components can be monitored, allowing us to separate each signal into a component attributed to the external driving force and one to the internal dynamics. We propose a formalism to capture the potential multiscaling in the fluctuations and apply it to the high-frequency trading records of the New York Stock Exchange. We find that on the time scale of minutes the dynamics is governed by internal processes, while on a daily or longer scale the external factors dominate. This transition from internal to external dynamics induces systematic changes in the scaling exponents, offering direct evidence of non-universality in the system.
Barabasi

M. A. de Menezes, A.-L. Barabási

Separating the internal and external dynamics of complex systems

Physical Review Letters 93, 68701 (2004)

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The observable behavior of a complex system reflects the mechanisms governing the internal interactions between the system’s components and the effect of external perturbations. Here we show that by capturing the simultaneous activity of several of the system’s components we can separate the internal dynamics from the external fluctuations. The method allows us to systematically determine the origin of fluctuations in various real systems, finding that while the Internet and the computer chip have robust internal dynamics, highway and Web traffic are driven by external demand. As multichannel measurements are becoming the norm in most fields, the method could help uncover the collective dynamics of a wide array of complex systems.