Amar Dhand, Liam McCafferty, Rachel Grashow, Ian M. Corbin, Sarah Cohan, Alicia J. Whittington, Ann Connor, Aaron Baggish, Mark Weisskopf, Ross Zafonte, Alvaro Pascual-Leone & Albert-László Barabási
Social network structure and composition in former NFL football players
Scientific Reports volume 11, Article number: 1630 (2021)
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Social networks have broad effects on health and quality of life. Biopsychosocial factors may also modify the effects of brain trauma on clinical and pathological outcomes. However, social network characterization is missing in studies of contact sports athletes. Here, we characterized the personal social networks of former National Football League players compared to non-football US males. In 303 former football players and 269 US males, we found that network structure (e.g., network size) did not differ, but network composition (e.g., proportion of family versus friends) did differ. Football players had more men than women, and more friends than family in their networks compared to US males. Black players had more racially diverse networks than White players and US males. These results are unexpected because brain trauma and chronic illnesses typically cause diminished social relationships. We anticipate our study will inform more multi-dimensional study of, and treatment options for, contact sports athletes. For example, the strong allegiances of former athletes may be harnessed in the form of social network interventions after brain trauma. Because preserving health of contact sports athletes is a major goal, the study of social networks is critical to the design of future research and treatment trials.
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.
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.
I. A. Kovács, A.-L. Barabási
Destruction perfected
Nature (News & Views) 524, 38-39 (2015)
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Pinpointing the nodes whose removal most effectively disrupts a network has become a lot easier with the development of an efficient algorithm. Potential applications might include cybersecurity and disease control. See Letter p.65, by F. Morone and H. A. Makse (Supplementary 1).
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.
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.
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
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.
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.
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.
A.-L. Barabási, C. Song, D. Wang
Handful of papers dominates citation
Nature 491, 40 (2012)
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An ‘impact disparity’ is emerging in science — only a few papers earn the largest share of citations. This is comparable to the income disparity in the United States, known as the 1% phenomenon, where 1% of the population earns a disproportionate 17.4% of total income.
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.
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.
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.
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.
G. Ghoshal, A.-L. Barabási
Ranking stability and super-stable nodes in complex networks
Nature Communications 2, 1-7 (2011)
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Pagerank, a network-based diffusion algorithm, has emerged as the leading method to rank web content, ecological species and even scientists. Despite its wide use, it remains unknown how the structure of the network on which it operates affects its performance. Here we show that for random networks the ranking provided by pagerank is sensitive to perturbations in the network topology, making it unreliable for incomplete or noisy systems. In contrast, in scale-free networks we predict analytically the emergence of super-stable nodes whose ranking is exceptionally stable to perturbations. We calculate the dependence of the number of super-stable nodes on network characteristics and demonstrate their presence in real networks, in agreement with the analytical predictions. These results not only deepen our understanding of the interplay between network topology and dynamical processes but also have implications in all areas where ranking has a role, from science to marketing.
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.
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.
M. Karsai, M. Kivelä, R. K. Pan, K. Kaski, J. Kertész, A.-L. Barabási, J. Saramäki
Small but slow world: How network topology and burstiness slow down spreading
Physical Review E 83, 1-4 (2011)
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While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the susceptible-infected model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.
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.
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.
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.
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.
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.
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.
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.
J.-P. Onnela, J. Saramaki, J. Hyvonen, G. Szabo, D. Lazer, K. Kaski, J. Kertesz, A.-L. Barabási
Structure and tie strengths in mobile communication networks
Proceedings of the National Academy of Sciences 104 (18), 7332-7336 (2007)
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Electronic databases, from phone to e-mails logs, currently provide detailed records of human communication patterns, offering novel avenues to map and explore the structure of social and communication networks. Here we examine the communication patterns of millions of mobile phone users, allowing us to simultaneously study the local and the global structure of a society-wide communication network. We observe a coupling between interaction strengths and the network's local structure, with the counterintuitive consequence that social networks are robust to the removal of the strong ties but fall apart after a phase transition if the weak ties are removed. We show that this coupling significantly slows the diffusion process, resulting in dynamic trapping of information in communities and find that, when it comes to information diffusion, weak and strong ties are both simultaneously ineffective.
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.
G. Madey, G. Szabo, A.-L. Barabási
WIPER: the integrated wireless phone based emergency response system
Lecture Notes in Computer Science 3993, 417-424 (2006)
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We describe a prototype emergency response system. This dynamic data driven application system (DDDAS) uses wireless call data, including call volume, who calls whom, call duration, services in use, and cell phone location information. Since all cell phones (that are powered on) maintain contact with one or more local cell towers, location data about each phone is updated periodically and available throughout the cellular phone network. This permits the cell phones of a city to serve as an ad hoc mobile sensor net, measuring the movement and calling patterns of the population. Social network theory and statistical analysis on normal call activity and call locations establish a baseline. A detection and alert system monitors streaming summary cell phone call data. Abnormal call patterns or population movements trigger a simulation and prediction system. Hypotheses about the anomaly are generated by a rule-based system, each initiating an agent-based simulation. Automated dynamic validation of the simulations against incoming streaming data is used to test each hypothesis. A validated simulation is used to predict the evolution of the anomaly and made available to an emergency response decision support system.
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.
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.
A.-L. Barabási
Network theory-the emergence of creative enterprise
Science 308, 639 (2005)
H. Jeong, Z. Neda, A.-L. Barabási
Measuring preferential attachment in evolving networks
Europhysics Letters 61, 567-572 (2003)
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A key ingredient of many current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called preferential attachment. Measurements on four networks, namely the science citation network, Internet, actor collaboration and science coauthorship network indicate that the rate at which nodes acquire links depends on the node’s degree, offering direct quantitative support for the presence of preferential attachment. We find that for the first two systems the attachment rate depends linearly on the node degree, while for the last two the dependence follows a sublinear power law.
A.L. Barabási, H. Jeong, Z. Neda, E. Ravasz, A. Schubert, T. Vicsek
Evolution of the social network of scientific collaborations
Physica A 311, 590-614 (2002)
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The co-authorship network of scientists represents a prototype of complex evolving networks. In addition, it o8ers one of the most extensive database to date on social networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an 8-year period (1991–98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. Three complementary approaches allow us to obtain a detailed characterization. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, a8ecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network’s time evolution. In some limits the model can be solved analytically, predicting a two-regime scaling in agreement with the measurements. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically. The combined numerical and analytical results underline the important role internal links play in determining the observed scaling behavior and network topology. The results and methodologies developed in the context of the co-authorship network could be useful for a systematic study of other complex evolving networks as well, such as the world wide web, Internet, or other social networks.