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.
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.
O. Rozenblatt-Rosen, R. C. Deo, M. Padi, G. Adelmant, T. Rolland, M. Grace, A. Dricot, M. Askenazi, M. Tavares, S. J. Pevzner, F. Abderazzaq, D. Byrdsong, A.-R. Carvunis, A. A. Chen, J. Cheng, M. Correll, M. Durate, C. Fan, M. C. Feltkamp, S. B. Ficarro, R. Franchi, B. K. Garg, N. Gulbahce, T. Hao, A. M. Holthaus, R. James, A. Korkhin, L. Litovchick, J. C. Mar, T. R. Pak, S. Rabello, R. Rubio, Y. Shen, S. Singh, J. M. Spangle, M. Tasan, S. Wanamakter, J. T. Webber, J. Roecklein-Canfield,, E. Johannsen, A.-L. Barabasi,, R. Beroukhim, E. Kieff,, M. E. Cusick, D. E. Hill,, K. Munger, J. A. Marto,, J. Quackenbush, F. P. Roth,, J. A. DeCaprio, M. Vidal
Interpreting cancer genomes using systematic host network perturbations by tumour virus proteins
Nature 487, 491-495 (2012)
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Genotypic differences greatly influence susceptibility and resistance to disease. Understanding genotype–phenotype relationships requires that phenotypes be viewed as manifestations of network properties, rather than simply as the result of individual genomic variations. Genome sequencing efforts have identified numerous germline mutations, and large numbers of somatic genomic alterations, associated with a predisposition to cancer. However, it remains difficult to distinguish background, or ‘passenger’, cancer mutations from causal, or ‘driver’, mutations in these data sets. Human viruses intrinsically depend on their host cell during the course of infection and can elicit pathological phenotypes similar to those arising from mutations. Here we test the hypothesis that genomic variations and tumour viruses may cause cancer through related mechanisms, by systematically examining host interactome and transcriptome network perturbations caused by DNA tumour virus proteins. The resulting integrated viral perturbation data reflects rewiring of the host cell networks, and highlights pathways, such as Notch signalling and apoptosis, that go awry in cancer. We show that systematic analyses of host targets of viral proteins can identify cancer genes with a success rate on a par with their identification through functional genomics and large-scale cataloguing of tumour mutations. Together, these complementary approaches increase the specificity of cancer gene identification. Combining systems-level studies of pathogen-encoded gene products with genomic approaches will facilitate the prioritization of cancer causing driver genes to advance the understanding of the genetic basis of human cancer.
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.
D. Wang, Z. Wen, H. Tong, C.-Y. Lin, C. Song, A.-L. Barabási
Information Spreading in Context
Proceeding for the 20th International World Wide Web Conference, 2011 , 1-10 (2011)
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Information spreading processes are central to human interactions. Despite recent studies in online domains, little is known about factors that could affect the dissemination of a single piece of information. In this paper, we address this challenge by combining two related but distinct datasets, collected from a large scale privacy-preserving distributed social sensor system. We find that the social and organizational context significantly impacts to whom and how fast people forward information. Yet the structures within spreading processes can be well captured by a simple stochastic branching model, indicating surprising independence of context. Our results build the foundation of future predictive models of information flow and provide significant insights towards design of communication platforms.
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.
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. Park, A-L. Barabási
Distribution of node characteristics in complex networks
Proceedings of the National Academy of Sciences 104, 17916-17920 (2007)
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Our enhanced ability to map the structure of various complex networks is increasingly accompanied by the possibility of independently identifying the functional characteristics of each node. Although this led to the observation that nodes with similar characteristics have a tendency to link to each other, in general we lack the tools to quantify the interplay between node properties and the structure of the underlying network. Here we show that when nodes in a network belong to two distinct classes, two independent parameters are needed to capture the detailed interplay between the network structure and node properties. We find that the network structure significantly limits the values of these parameters, requiring a phase diagram to uniquely characterize the configurations available to the system. The phase diagram shows a remarkable independence from the network size, a finding that, together with a proposed heuristic algorithm, allows us to determine its shape even for large networks. To test the usefulness of the developed methods, we apply them to biological and socioeconomic systems, finding that protein functions and mobile phone usage occupy distinct regions of the phase diagram, indicating that the proposed parameters have a strong discriminating power.
M. A. Yildirim, K.-L. Goh, M.E. Cusick, A.-L. Barabási, M. Vidal
Drug-target network
Nature Biotechnology 25:10, 1119-1126 (2007)
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The global set of relationships between protein targets of all drugs and all disease-gene products in the human protein–protein interaction or ‘interactome’ network remains uncharacterized. We built a bipartite graph composed of US Food and Drug Administration–approved drugs and proteins linked by drug–target binary associations. The resultingnetwork connects most drugs into a highly interlinked giant component, with strong local clustering of drugs of similar types according to Anatomical Therapeutic Chemical classification. Topological analyses of this network quantitatively showed an overabundance of ‘follow-on’ drugs, that is, drugs that target already targeted proteins. By including drugs currently under investigation, we identified a trend toward more functionally diverse targets improving polypharmacology. To analyze the relationships between drug targets and disease-gene products, we measured the shortest distance between both sets of proteins in current models of the human interactome network. Significant differences in distance were found between etiological and palliative drugs. A recent trend toward more rational drug design was observed.
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.
A.L. Barabási
Network Medicine — From Obesity to the “Diseasome”
New England Journal of Medicine 357, 404-407 (2007)
V. Vermeirssen, M. Inmaculada Barrasa, C. Hidalgo, J.-A. B. Babon, R. Sequerra, L. Doucette-Stamm, A.-L. Barabási, A. J.M. Walhout
Transcription factor modularity in a Gene-Centered C. elegans Protein-DNA interaction network
Genome Research 17, 061-1071 (2007)
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Transcription regulatory networks play a pivotal role in the development, function, and pathology of metazoan organisms. Such networks are comprised of protein–DNA interactions between transcription factors (TFs) and their target genes. An important question pertains to how the architecture of such networks relates to network functionality. Here, we show that a Caenorhabditis elegans core neuronal protein–DNA interaction network is organized into two TF modules. These modules contain TFs that bind to a relatively small number of target genes and are more systems specific than the TF hubs that connect the modules. Each module relates to different functional aspects of the network. One module contains TFs involved in reproduction and target genes that are expressed in neurons as well as in other tissues. The second module is enriched for paired homeodomain TFs and connects to target genes.
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.
K.-I. Goh, M. E. Cusick, D. Valle, B. Childs, M. Vidal, A.-L. Barabási
The human disease network
Proceedings of the National Academy of Sciences 104:21, 8685 (2007)
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A network of disorders and disease genes linked by known disorder–gene associations offers a platform to explore in a single graphtheoretic framework all known phenotype and disease gene associations, indicating the common genetic origin of many diseases. Genes associated with similar disorders show both higher likelihood of physical interactions between their products and higher expression profiling similarity for their transcripts, supporting the existence of distinct disease-specific functional modules. We find that essential human genes are likely to encode hub proteins and are expressed widely in most tissues. This suggests that disease genes also would play a central role in the human interactome. In contrast, we find that the vast majority of disease genes are nonessential and show no tendency to encode hub proteins, and their expression pattern indicates that they are localized in the functional periphery of the network. A selection-based model explains the observed difference between essential and disease genes and also suggests that diseases caused by somatic mutations should not be peripheral, a prediction we confirm for cancer genes.
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.
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.
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.
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.
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.
A.-L. Barabási, E. Bonabeau
Scale-Free Networks
Scientific American 288, 50-59 (2003)
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Scientists have recently discovered that various complex systems have an underlying architecture governed by shared organizing principies. This insight has important implications for a host of applications, from drug development to Internet security.
S. H. Yook, H. Jeong, A.-L. Barabási
Modeling the internet’s large-scale topology
Proceedings of the National Academy of Sciences 99, 13382-13386 (2002)
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Network generators that capture the Internet’s large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet’s evolution. By combining several independent databases capturing the time evolution, topology, and physical layout of the Internet, we identify the universal mechanisms that shape the Internet’s router and autonomous system level topology. We find that the physical layout of nodes form a fractal set, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently used exponential laws. The universal parameters that we extract significantly restrict the class of potentially correct Internet models and indicate that the networks created by all available topology generators are fundamentally different from the current Internet.
H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, A.-L. Barabási
The large-scale organization of metabolic networks
Nature 407, 651–655 (2000)
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Here we present a systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life.We show that, despite significant variation in their individual constituents and pathways, these metabolic networks have the same topological scaling properties and show striking similarities to the inherent organization of complex non-biological systems. This may indicate that metabolic organization is not only identical for all living organisms, but also complies with the design principles of robust and error-tolerant scale-free networks, and may represent a common blueprint for the large-scale organization of interactions among all cellular constituents.
A.-L. Barabási
The physics of the web
Physics World 14, 33-38 (2001)
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Statistical mechanics is offering new insights into the structure and dynamics of the Internet, the World Wide Web and other complex interacting systems. TH E INTERNET appears to have taken on a life of its own ever since the National Science foundation in the US gave up stewardship of the network in 1995. New lines and routers are added continually by thousands of companies, none of which require permission from anybody to do so, and none of which are obliged to report their activity. This uncontrolled and decentralized growth has turned network designers into scientific explorers. All previous Internet-related research concentrated on designing better protocols and faster components. More recently, an increasing number of scientists have begun to ask an unexpected question: what exactly did we create?'
R. Albert, H. Jeong, A.-L. Barabási
Error and attack tolerance of complex networks
Nature 406, 378–482 (2000)
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Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneouslywired networks,called scale-free networks, which include theWorld-WideWeb, the Internet, social networks and cells. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates.However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network’s connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.
H. Jeong, S. P. Mason, A.-L. Barabási, Z. N. Oltvai
Lethality and centrality in protein networks
Nature 411, 41-42 (2001)
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The most highly connected proteins in the cell are the most important for its survival. Proteins are traditionally identified on the basis of their individual actions as catalysts, signalling molecules, or building blocks in cells and microorganisms. But our post-genomic view is expanding the protein’s role into an element in a network of protein–protein interactions as well, in which it has a contextual or cellular function within functional modules1,2. Here we provide quantitative support for this idea by demonstrating that the phenotypic consequence of a single gene deletion in the yeast Saccharomyces cerevisiae is affected to a large extent by the topological position of its protein product in the complex hierarchical web of molecular interactions.
R. Albert, H. Jeong, A.-L. Barabási
Diameter of the world wide web
Nature 401, 130-131 (1999)
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Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the web’s connectivity and consequently how effectively we can locate information on it.
A.-L. Barabási, R. Albert, H. Jeong
Scale-free characteristics of random networks: the topology of the world wide web
Physica A 281, 69-77 (2000)
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The world-wide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scale-free characteristics. We introduce a model that leads to a scale-free network, capturing in a minimal fashion the self-organization processes governing the world-wide web.