Note to users. If you're seeing this message, it means that your browser cannot find this page's style/presentation instructions -- or possibly that you are using a browser that does not support current Web standards. Find out more about why this message is appearing, and what you can do to make your experience of our site the best it can be.

Science 15 October 1999:
Vol. 286. no. 5439, pp. 509 - 512
DOI: 10.1126/science.286.5439.509
Prev | Table of Contents | Next

Reports

Emergence of Scaling in Random Networks

Albert-László Barabási, * Réka Albert

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA.
*   To whom correspondence should be addressed. E-mail: alb{at}nd.edu

Read the Full Text


THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
Gene divergence and pathway duplication in the metabolic network of yeast and digital organisms.
P. Gerlee, T. Lundh, B. Zhang, and A. R. A. Anderson (2009)
J R Soc Interface 6, 1233-1245
   Abstract »    Full Text »    PDF »
Social Network Services as Data Sources and Platforms for e-Researching Social Networks.
R. Ackland (2009)
Social Science Computer Review 27, 481-492
   Abstract »    PDF »
Coexpression network based on natural variation in human gene expression reveals gene interactions and functions.
R. R. Nayak, M. Kearns, R. S. Spielman, and V. G. Cheung (2009)
Genome Res. 19, 1953-1962
   Abstract »    Full Text »    PDF »
Traffic-driven epidemic spreading in finite-size scale-free networks.
S. Meloni, A. Arenas, and Y. Moreno (2009)
PNAS 106, 16897-16902
   Abstract »    Full Text »    PDF »
Sick and edgy: walk-counting as a metric of epidemic spreading on networks.
D. C. Wylie and W. M. Getz (2009)
J R Soc Interface 6, 897-907
   Abstract »    Full Text »    PDF »
Network analyses in systems pharmacology.
S. I. Berger and R. Iyengar (2009)
Bioinformatics 25, 2466-2472
   Abstract »    Full Text »    PDF »
Spatio-temporal waves and targeted vaccination in recurrent epidemic network models.
A. Litvak-Hinenzon and L. Stone (2009)
J R Soc Interface 6, 749-760
   Abstract »    Full Text »    PDF »
Understanding spatial connectivity of individuals with non-uniform population density.
P. Wang and M. C. Gonzalez (2009)
Phil Trans R Soc A 367, 3321-3329
   Abstract »    Full Text »    PDF »
An investigation into the population abundance distribution of mRNAs, proteins, and metabolites in biological systems.
C. Lu and R. D. King (2009)
Bioinformatics 25, 2020-2027
   Abstract »    Full Text »    PDF »
Scaling laws of human interaction activity.
D. Rybski, S. V. Buldyrev, S. Havlin, F. Liljeros, and H. A. Makse (2009)
PNAS 106, 12640-12645
   Abstract »    Full Text »    PDF »
Scale-Free Networks: A Decade and Beyond.
A.-L. Barabasi (2009)
Science 325, 412-413
   Abstract »    Full Text »    PDF »
Predicting the Behavior of Techno-Social Systems.
A. Vespignani (2009)
Science 325, 425-428
   Abstract »    Full Text »    PDF »
Degree dependence in rates of transcription factor evolution explains the unusual structure of transcription networks.
A. J. Stewart, R. M. Seymour, and A. Pomiankowski (2009)
Proc R Soc B 276, 2493-2501
   Abstract »    Full Text »    PDF »
Theoretical framework for the histone modification network: modifications in the unstructured histone tails form a robust scale-free network.
Y. Hayashi, T. Senda, N. Sano, and M. Horikoshi (2009)
Genes Cells 14, 789-806
   Abstract »    Full Text »    PDF »
Model criticism based on likelihood-free inference, with an application to protein network evolution.
O. Ratmann, C. Andrieu, C. Wiuf, and S. Richardson (2009)
PNAS 106, 10576-10581
   Abstract »    Full Text »    PDF »
Food-web structure and ecosystem services: insights from the Serengeti.
A. Dobson (2009)
Phil Trans R Soc B 364, 1665-1682
   Abstract »    Full Text »    PDF »
The assembly and disassembly of ecological networks.
J. Bascompte and D. B. Stouffer (2009)
Phil Trans R Soc B 364, 1781-1787
   Abstract »    Full Text »    PDF »
KELLER: estimating time-varying interactions between genes.
L. Song, M. Kolar, and E. P. Xing (2009)
Bioinformatics 25, i128-i136
   Abstract »    Full Text »    PDF »
The Lexical Restructuring Hypothesis and Graph Theoretic Analyses of Networks Based on Random Lexicons.
T. M. Gruenenfelder and D. B. Pisoni (2009)
J Speech Lang Hear Res 52, 596-609
   Abstract »    Full Text »    PDF »
Transcriptional regulation shapes the organization of genes on bacterial chromosomes.
S. C. Janga, H. Salgado, and A. Martinez-Antonio (2009)
Nucleic Acids Res. 37, 3680-3688
   Abstract »    Full Text »    PDF »
Global networks of functional coupling in eukaryotes from comprehensive data integration.
A. Alexeyenko and E. L.L. Sonnhammer (2009)
Genome Res. 19, 1107-1116
   Abstract »    Full Text »    PDF »
Uniting pattern and process in plant-animal mutualistic networks: a review.
D. P. Vazquez, N. Bluthgen, L. Cagnolo, and N. P. Chacoff (2009)
Ann. Bot. 103, 1445-1457
   Abstract »    Full Text »    PDF »
The effect of network topology on the stability of discrete state models of genetic control.
A. Pomerance, E. Ott, M. Girvan, and W. Losert (2009)
PNAS 106, 8209-8214
   Abstract »    Full Text »    PDF »
Using Complex Networks to Model Two- and Three-Dimensional Soil Porous Architecture.
S. J. Mooney and D. Korosak (2009)
Soil Sci. Soc. Am. J. 73, 1094-1100
   Abstract »    Full Text »    PDF »
Noninjurious mechanical ventilation activates a proinflammatory transcriptional program in the lung.
S. A. Gharib, W. C. Liles, L. S. Klaff, and W. A. Altemeier (2009)
Physiol Genomics 37, 239-248
   Abstract »    Full Text »    PDF »
Changing Neighborhoods--Neighborhoods Changing: A Framework for Spatially Explicit Agent-Based Models of Social Systems.
D. O'Sullivan (2009)
Sociological Methods Research 37, 498-530
   Abstract »    PDF »
Domain mobility in proteins: functional and evolutionary implications.
M. K. Basu, E. Poliakov, and I. B. Rogozin (2009)
Brief Bioinform 10, 205-216
   Abstract »    Full Text »    PDF »
Using Semantic and Structural Properties of the Unified Medical Language System to Discover Potential Terminological Relationships.
C. O. Patel and J. J. Cimino (2009)
J. Am. Med. Inform. Assoc. 16, 346-353
   Abstract »    Full Text »    PDF »
In Silico Analysis of Phosphoproteome Data Suggests a Rich-get-richer Process of Phosphosite Accumulation over Evolution.
N. Yachie, R. Saito, J. Sugahara, M. Tomita, and Y. Ishihama (2009)
Mol. Cell. Proteomics 8, 1061-1071
   Abstract »    Full Text »    PDF »
The spread of awareness and its impact on epidemic outbreaks.
S. Funk, E. Gilad, C. Watkins, and V. A. A. Jansen (2009)
PNAS 106, 6872-6877
   Abstract »    Full Text »    PDF »
Extracting the multiscale backbone of complex weighted networks.
M. A. Serrano, M. Boguna, and A. Vespignani (2009)
PNAS 106, 6483-6488
   Abstract »    Full Text »    PDF »
Solitonets: complex networks of interacting fields.
I. Kaminer, M. Segev, A. M Bruckstein, and Y. C Eldar (2009)
Proc R Soc A 465, 1093-1101
   Abstract »    Full Text »    PDF »
The Time-Series Link Prediction Problem with Applications in Communication Surveillance.
Z. Huang and D. K. J. Lin (2009)
INFORMS Journal on Computing 21, 286-303
   Abstract »    PDF »
Benchmarking regulatory network reconstruction with GRENDEL.
B. C. Haynes and M. R. Brent (2009)
Bioinformatics 25, 801-807
   Abstract »    Full Text »    PDF »
Clustering in a network of non-identical and mutually interacting agents.
F. De Smet and D. Aeyels (2009)
Proc R Soc A 465, 745-768
   Abstract »    Full Text »    PDF »
Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks.
C.-Y. Huang, Y.-S. Tsai, C.-T. Sun, J.-L. Hsieh, and C.-Y. Cheng (2009)
SIMULATION 85, 205-219
   Abstract »    PDF »
Elucidating the Role of Gonadal Hormones in Sexually Dimorphic Gene Coexpression Networks.
A. van Nas, D. GuhaThakurta, S. S. Wang, N. Yehya, S. Horvath, B. Zhang, L. Ingram-Drake, G. Chaudhuri, E. E. Schadt, T. A. Drake, et al. (2009)
Endocrinology 150, 1235-1249
   Abstract »    Full Text »    PDF »
Gclust: trans-kingdom classification of proteins using automatic individual threshold setting.
N. Sato (2009)
Bioinformatics 25, 599-605
   Abstract »    Full Text »    PDF »
Insights into the Organization of Biochemical Regulatory Networks Using Graph Theory Analyses.
A. Ma'ayan (2009)
J. Biol. Chem. 284, 5451-5455
   Abstract »    Full Text »    PDF »
From the Cover: Model of genetic variation in human social networks.
J. H. Fowler, C. T. Dawes, and N. A. Christakis (2009)
PNAS 106, 1720-1724
   Abstract »    Full Text »    PDF »
Representing the UK's cattle herd as static and dynamic networks.
M. C Vernon and M. J Keeling (2009)
Proc R Soc B 276, 469-476
   Abstract »    Full Text »    PDF »
Behavioral experiments on biased voting in networks.
M. Kearns, S. Judd, J. Tan, and J. Wortman (2009)
PNAS 106, 1347-1352
   Abstract »    Full Text »    PDF »
WiFi networks and malware epidemiology.
H. Hu, S. Myers, V. Colizza, and A. Vespignani (2009)
PNAS 106, 1318-1323
   Abstract »    Full Text »    PDF »
Towards safer, better healthcare: harnessing the natural properties of complex sociotechnical systems.
J Braithwaite, W B Runciman, and A F Merry (2009)
Qual. Saf. Health Care 18, 37-41
   Abstract »    Full Text »    PDF »
Identification of candidate disease genes by integrating Gene Ontologies and protein-interaction networks: case study of primary immunodeficiencies.
C. Ortutay and M. Vihinen (2009)
Nucleic Acids Res. 37, 622-628
   Abstract »    Full Text »    PDF »
Comparative analysis of the packing topology of structurally important residues in helical membrane and soluble proteins.
V. Pabuwal and Z. Li (2009)
Protein Eng. Des. Sel. 22, 67-73
   Abstract »    Full Text »    PDF »
Folding energy landscape and network dynamics of small globular proteins.
N. Hori, G. Chikenji, R. S. Berry, and S. Takada (2009)
PNAS 106, 73-78
   Abstract »    Full Text »    PDF »
Universities-Industry Links and Regional Development in Japan: Connecting Excellence and Relevance? .
F. Kitagawa (2009)
Science Technology and Society 14, 1-33
   Abstract »    PDF »
Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease.
C. J. Stam, W. de Haan, A. Daffertshofer, B. F. Jones, I. Manshanden, A. M. van Cappellen van Walsum, T. Montez, J. P. A. Verbunt, J. C. de Munck, B. W. van Dijk, et al. (2009)
Brain 132, 213-224
   Abstract »    Full Text »    PDF »
Translational Biology: From Arabidopsis Flowers to Grass Inflorescence Architecture.
B. E. Thompson and S. Hake (2009)
Plant Physiology 149, 38-45
   Full Text »    PDF »
Superfamily phenomena and motifs of networks induced from time series.
X. Xu, J. Zhang, and M. Small (2008)
PNAS 105, 19601-19605
   Abstract »    Full Text »    PDF »
Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks.
A. Ma'ayan, G. A. Cecchi, J. Wagner, A. R. Rao, R. Iyengar, and G. Stolovitzky (2008)
PNAS 105, 19235-19240
   Abstract »    Full Text »    PDF »
The effect of opinion clustering on disease outbreaks.
M. Salathe and S. Bonhoeffer (2008)
J R Soc Interface 5, 1505-1508
   Abstract »    Full Text »    PDF »
Laws of population growth.
H. D. Rozenfeld, D. Rybski, J. S. Andrade Jr., M. Batty, H. E. Stanley, and H. A. Makse (2008)
PNAS 105, 18702-18707
   Abstract »    Full Text »    PDF »
A Small World of Neuronal Synchrony.
S. Yu, D. Huang, W. Singer, and D. Nikolic (2008)
Cereb Cortex 18, 2891-2901
   Abstract »    Full Text »    PDF »
Analysis of copy number variants and segmental duplications in the human genome: Evidence for a change in the process of formation in recent evolutionary history.
P. M. Kim, H. Y.K. Lam, A. E. Urban, J. O. Korbel, J. Affourtit, F. Grubert, X. Chen, S. Weissman, M. Snyder, and M. B. Gerstein (2008)
Genome Res. 18, 1865-1874
   Abstract »    Full Text »    PDF »
The Protein Interaction Network of the Epithelial Junctional Complex: A System-Level Analysis.
L. Paris and G. Bazzoni (2008)
Mol. Biol. Cell 19, 5409-5421
   Abstract »    Full Text »    PDF »
Phylogenetic distances are encoded in networks of interacting pathways.
A. Mazurie, D. Bonchev, B. Schwikowski, and G. A. Buck (2008)
Bioinformatics 24, 2579-2585
   Abstract »    Full Text »    PDF »
From the Cover: Asymmetric disassembly and robustness in declining networks.
S. Saavedra, F. Reed-Tsochas, and B. Uzzi (2008)
PNAS 105, 16466-16471
   Abstract »    Full Text »    PDF »
Convergence and divergence are mostly reciprocated properties of the connections in the network of cortical areas.
L. Negyessy, T. Nepusz, L. Zalanyi, and F. Bazso (2008)
Proc R Soc B 275, 2403-2410
   Abstract »    Full Text »    PDF »
An analysis of the fixation probability of a mutant on special classes of non-directed graphs.
M Broom and J Rychtar (2008)
Proc R Soc A 464, 2609-2627
   Abstract »    Full Text »    PDF »
High-Quality Binary Protein Interaction Map of the Yeast Interactome Network.
H. Yu, P. Braun, M. A. Yildirim, I. Lemmens, K. Venkatesan, J. Sahalie, T. Hirozane-Kishikawa, F. Gebreab, N. Li, N. Simonis, et al. (2008)
Science 322, 104-110
   Abstract »    Full Text »    PDF »
From the Cover: Experience versus talent shapes the structure of the Web.
J. S. Kong, N. Sarshar, and V. P. Roychowdhury (2008)
PNAS 105, 13724-13729
   Abstract »    Full Text »    PDF »
OR FORUM--Catching the "Network Science" Bug: Insight and Opportunity for the Operations Researcher.
D. L. Alderson (2008)
Operations Research 56, 1047-1065
   Abstract »    PDF »
Editorial Overview--The Interplay Between Digital and Social Networks.
R. Agarwal, A. K. Gupta, and R. Kraut (2008)
Information Systems Research 19, 243-252
   Abstract »    PDF »
Emergence of New Project Teams from Open Source Software Developer Networks: Impact of Prior Collaboration Ties.
J. Hahn, J. Y. Moon, and C. Zhang (2008)
Information Systems Research 19, 369-391
   Abstract »    PDF »
The Effects of the Social Structure of Digital Networks on Viral Marketing Performance.
M. Bampo, M. T. Ewing, D. R. Mather, D. Stewart, and M. Wallace (2008)
Information Systems Research 19, 273-290
   Abstract »    PDF »
Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems.
A. Wilson (2008)
J R Soc Interface 5, 865-871
   Abstract »    Full Text »    PDF »
Extremism Propagation in Social Networks with Hubs.
D. W. Franks, J. Noble, P. Kaufmann, and S. Stagl (2008)
Adaptive Behavior 16, 264-274
   Abstract »    PDF »
Emergence and Robustness of a Community Discussion Network on Mercury Contamination and Health in the Brazilian Amazon.
F. Mertens, J. Saint-Charles, M. Lucotte, and D. Mergler (2008)
Health Educ Behav 35, 509-521
   Abstract »    PDF »
Bibliometrics to webometrics.
M. Thelwall (2008)
Journal of Information Science 34, 605-621
   Abstract »    PDF »
Revealing unique properties of the ribosome using a network based analysis.
H. David-Eden and Y. Mandel-Gutfreund (2008)
Nucleic Acids Res. 36, 4641-4652
   Abstract »    Full Text »    PDF »
Cozzarelli Prize Winner@;DELIM@;From the Cover: The implications of human metabolic network topology for disease comorbidity.
D.-S. Lee, J. Park, K. A. Kay, N. A. Christakis, Z. N. Oltvai, and A.-L. Barabasi (2008)
PNAS 105, 9880-9885
   Abstract »    Full Text »    PDF »
Electronic Publication and the Narrowing of Science and Scholarship.
J. A. Evans (2008)
Science 321, 395-399
   Abstract »    Full Text »    PDF »
Geometric constraints on neuronal connectivity facilitate a concise synaptic adhesive code.
S. Itzkovitz, L. Baruch, E. Shapiro, and E. Segal (2008)
PNAS 105, 9278-9283
   Abstract »    Full Text »    PDF »
Genetic-linkage mapping of complex hereditary disorders to a whole-genome molecular-interaction network.
I. Iossifov, T. Zheng, M. Baron, T. C. Gilliam, and A. Rzhetsky (2008)
Genome Res. 18, 1150-1162
   Abstract »    Full Text »    PDF »
Biomolecular network motif counting and discovery by color coding.
N. Alon, P. Dao, I. Hajirasouliha, F. Hormozdiari, and S. C. Sahinalp (2008)
Bioinformatics 24, i241-i249
   Abstract »    Full Text »    PDF »
Topological modelling of large networks.
R. J Mondragon (2008)
Phil Trans R Soc A 366, 1931-1940
   Abstract »    Full Text »    PDF »
Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models.
H. Rahmandad and J. Sterman (2008)
Management Science 54, 998-1014
   Abstract »    PDF »
From the Cover: Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures.
R. J. Morgan and I. Soltesz (2008)
PNAS 105, 6179-6184
   Abstract »    Full Text »    PDF »
MMG: a probabilistic tool to identify submodules of metabolic pathways.
G. Sanguinetti, J. Noirel, and P. C. Wright (2008)
Bioinformatics 24, 1078-1084
   Abstract »    Full Text »    PDF »
Fitting a geometric graph to a protein-protein interaction network.
D. J. Higham, M. Rasajski, and N. Przulj (2008)
Bioinformatics 24, 1093-1099
   Abstract »    Full Text »    PDF »
What Can Graph Theory Tell Us About Word Learning and Lexical Retrieval?.
M. S. Vitevitch (2008)
J Speech Lang Hear Res 51, 408-422
   Abstract »    Full Text »    PDF »
From time series to complex networks: The visibility graph.
L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuno (2008)
PNAS 105, 4972-4975
   Abstract »    Full Text »    PDF »
Biological pathway kinetic rate constants are scale-invariant.
S. Grandison and R. J. Morris (2008)
Bioinformatics 24, 741-743
   Abstract »    Full Text »    PDF »


To Advertise     Find Products

Science. ISSN 0036-8075 (print), 1095-9203 (online)