Networks, Dynamics, and the Small‐World Phenomenon
Abstract
The small‐world phenomenon formalized in this article as the coincidence of high local clustering and short global separation, is shown to be a general feature of sparse, decentralized networks that are neither completely ordered nor completely random. Networks of this kind have received little attention, yet they appear to be widespread in the social and natural sciences, as is indicated here by three distinct examples. Furthermore, small admixtures of randomness to an otherwise ordered network can have a dramatic impact on its dynamical, as well as structural, properties‐a feature illustrated by a simple model of disease transmission.
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The structure of the nervous system of the nematode <i>Caenorhabditis elegans</i>
White, J. G., Southgate, E., Thomson, J. N., & Brenner, S. (1986) · Philosophical Transactions of the Royal Society of London. B, Biological Sciences · doi:10.1098/rstb.1986.0056 · Cited by 5,589 · see citing works
Constraints on cortical and thalamic projections: the no-strong-loops hypothesis
Crick, F., & Koch, C. (1998) · Nature · doi:10.1038/34584 · Cited by 353 · cited 2× · see citing works
“Furthermore, small admixtures of randomness to an otherwise ordered network can have a dramatic impact on its dynamical, as well as structural, properties—a feature illustrated by a simple model of disease transmission.”
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Structural Holes and Good Ideas
Burt, R. S. (2004) · American Journal of Sociology · doi:10.1086/421787 · Cited by 5,642 · see citing works
From Isovists to Visibility Graphs: A Methodology for the Analysis of Architectural Space
Turner, A., Doxa, M., O'Sullivan, D., & Penn, A. (2001) · Environment and Planning B: Planning and Design · doi:10.1068/b2684 · Cited by 969 · see citing works
A Weighted and Directed Interareal Connectivity Matrix for Macaque Cerebral Cortex
Markov, N. T., Ercsey-Ravasz, M. M., Ribeiro Gomes, A. R., Lamy, C., Magrou, L., Vezoli, J., Misery, P., Falchier, A., Quilodran, R., Gariel, M. A., et al. (2014) · Cerebral Cortex · doi:10.1093/cercor/bhs270 · Cited by 857 · see citing works
The Network Structure of Exploration and Exploitation
Lazer, D., & Friedman, A. (2007) · Administrative Science Quarterly · doi:10.2189/asqu.52.4.667 · Cited by 696 · see citing works
A Predictive Network Model of Cerebral Cortical Connectivity Based on a Distance Rule
Ercsey-Ravasz, M., Markov, N. T., Lamy, C., Van Essen, D. C., Knoblauch, K., Toroczkai, Z., & Kennedy, H. (2013) · Neuron · doi:10.1016/j.neuron.2013.07.036 · Cited by 487 · see citing works
Maximal planar networks with large clustering coefficient and power-law degree distribution
Zhou, T., Yan, G., & Wang, B.-H. (2005) · Physical Review E · doi:10.1103/physreve.71.046141 · Cited by 265 · see citing works
The Decline of the Death Penalty and the Discovery of Innocence
Baumgartner, F. R., De Boef, S. L., & Boydstun, A. E. (2001) · Cambridge University Press · doi:10.1017/cbo9780511790638 · Cited by 242 · see citing works
Small Worlds and Cultural Polarization
FLACHE, A., & MACY, M. W. (2011) · The Journal of Mathematical Sociology · doi:10.1080/0022250x.2010.532261 · Cited by 237 · see citing works
Staber, U. (2001) · Regional Studies · doi:10.1080/00343400125106 · Cited by 201 · see citing works
Complex networks from classical to quantum
Biamonte, J., Faccin, M., & De Domenico, M. (2019) · Communications Physics · doi:10.1038/s42005-019-0152-6 · Cited by 149 · see citing works
Better with Age? Tie Longevity and the Performance Implications of Bridging and Closure
Baum, J. A. C., McEvily, B., & Rowley, T. J. (2012) · Organization Science · doi:10.1287/orsc.1100.0566 · Cited by 133 · see citing works
Multistart Methods for Quantum Approximate optimization
Shaydulin, R., Safro, I., & Larson, J. (2019) · 2019 IEEE High Performance Extreme Computing Conference (HPEC) · doi:10.1109/hpec.2019.8916288 · Cited by 110 · see citing works
Strategy evolution on dynamic networks
Su, Q., McAvoy, A., & Plotkin, J. B. (2023) · Nature Computational Science · doi:10.1038/s43588-023-00509-z · Cited by 88 · see citing works
Trust and partner selection in social networks: An experimentally grounded model
Bravo, G., Squazzoni, F., & Boero, R. (2012) · Social Networks · doi:10.1016/j.socnet.2012.03.001 · Cited by 85 · see citing works
“In the smallWorld model, we introduced a fixed “small-world” network structure (Watts & Strogatz 1998; Watts 1999) with initial degree 4 and re-wiring probability 0.01.”
MethodResultInfluentialThe Role of Ego Networks in Manufacturing Joint Venture Formations
Carnovale, S., & Yeniyurt, S. (2014) · Journal of Supply Chain Management · doi:10.1111/jscm.12015 · Cited by 70 · see citing works
Introduction to Special Issue: The Consumer in a Connected World
Deighton, J., Goldenberg, J., & Stephen, A. T. (2017) · Journal of the Association for Consumer Research · doi:10.1086/691974 · Cited by 3 · see citing works
Nomura, K., & Horii, T. (2026) · ALIFE 2026: Proceedings of the 2026 Artificial Life Conference · doi:10.1162/isal.a.1009
Social Reality Construction via Active Inference: Modeling the Dialectic of Conformity and Creativity
Nomura, K., & Horii, T. (2026) · arXiv
“The experiments were conducted on a connected caveman graph (Watts, 1999) comprising K = 14 agents.”
- Authors
- Watts, D. J.
- Affiliations
- Santa Fe Institute (US)
- Corresponding author
- Watts, Duncan J.
- ORCID
- Watts, Duncan J.
- Venue
- American Journal of Sociology
- Publisher
- University of Chicago Press
- Published
- 1999-09
- Volume
- 105
- Issue
- 2
- Pages
- 493-527
- ISSN
- 0002-9602 (ISSN-L)
- 1537-5390
- OpenAlex
- W2002470750
- Cited by
- 1,510
- References
- 2
- Citations by year
- 2026: 32 · 2025: 43 · 2024: 38 · 2023: 57 · 2022: 51 · 2021: 112 · 2020: 81 · 2019: 51 · 2018: 78 · 2017: 55 · 2016: 63 · 2015: 70 · 2014: 77 · 2013: 88 · 2012: 68
- FWCI
- 10.74
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Sociology (publishedVersion)
- American Journal of Sociology
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Opinion Dynamics and Social Influence
- Physical Sciences › Mathematics › Geometry and Topology › Graph theory and applications
- Keywords
- small-world networks, local clustering, network dynamics, disease transmission modeling, social networks, network structure
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