Collective Dynamics of 'Small-World' Networks¶
Watts, D. J., & Strogatz, S. H. (1998). Collective Dynamics of 'Small-World' Networks. Nature, 393(6684), 440-442.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Cultural Diffusion
This sourceShows that rewiring a small fraction of edges into long-range links collapses average path length while preserving local clustering. (Discussed by name in prose but never cited via a footnote marker — )
- Network
- … problem (founding graph theory by abstracting the city's geography to nodes and edges), matured through Erdős and Rényi's 1959 random-graph model (the first rigorous probabilistic theory of large graphs), was transformed by Milgram's 1967 small-world experiment, Watts and Strogatz's 1998 small-world network model
This sourceShows that rewiring a tiny fraction of edges into long-range links collapses average path length while leaving local clustering nearly intact; supports the small-world formalization, the bridge-versus-redundancy complexity compression, the claim that adding a non-redundant link shrinks effective distance faster than strengthening one, and the small-world rewiring example.
- … problem (founding graph theory by abstracting the city's geography to nodes and edges), matured through Erdős and Rényi's 1959 random-graph model (the first rigorous probabilistic theory of large graphs), was transformed by Milgram's 1967 small-world experiment, Watts and Strogatz's 1998 small-world network model
- Non-Locality
- In network science, the long-range "shortcut" edges of a small-world graph are non-local by construction: they connect nodes far apart in the underlying lattice, and it is precisely these few non-local edges that collapse path lengths and create the small-world property.
This sourceShows that adding a few long-range (non-local) shortcut edges to a ring lattice collapses average path length from linear to logarithmic while barely changing local clustering.
Supported in partVerified against the publisher's abstract
The abstract states the small-world result — rewired regular networks stay highly clustered yet take on short characteristic path lengths — but never uses 'non-local' and gives no measure of the path-length collapse.
“We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon”
- In network science, the long-range "shortcut" edges of a small-world graph are non-local by construction: they connect nodes far apart in the underlying lattice, and it is precisely these few non-local edges that collapse path lengths and create the small-world property.
- Propagation
- A network engineer familiar with wave dispersion and reflection might recognize parallel patterns in social networks; an epidemiologist familiar with R₀ might see the same exponential growth structure in tech adoption or misinformation, an isomorphism Watts and Strogatz (1998) made tractable by showing that small-world structure governs spreading dynamics across biological, technological, and social networks alike.
This sourceShows that rewiring a tiny fraction of edges into long-range links collapses average path length while leaving local clustering nearly intact; supports the small-world formalization, the bridge-versus-redundancy complexity compression, the claim that adding a non-redundant link shrinks effective distance faster than strengthening one, and the small-world rewiring example.
Supported in partVerified against the publisher's abstract
The abstract confirms biological, technological and social networks are small-world and that small-world coupling speeds propagation in models, but it does not show small-world structure governing spreading in all three domains alike.
“The neural network of the worm Caenorhabditis elegans , the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular …”
- A network engineer familiar with wave dispersion and reflection might recognize parallel patterns in social networks; an epidemiologist familiar with R₀ might see the same exponential growth structure in tech adoption or misinformation, an isomorphism Watts and Strogatz (1998) made tractable by showing that small-world structure governs spreading dynamics across biological, technological, and social networks alike.
- Threshold-Driven Order Emergence
- Within twelve months, two of the three cities cross their local thresholds and adopt the target policy; the resulting political visibility triggers cascading adoption among nearby cities.
This sourceShows that rewiring a tiny fraction of edges into long-range links collapses average path length while leaving local clustering nearly intact; supports the small-world formalization, the bridge-versus-redundancy complexity compression, the claim that adding a non-redundant link shrinks effective distance faster than strengthening one, and the small-world rewiring example.
- Within twelve months, two of the three cities cross their local thresholds and adopt the target policy; the resulting political visibility triggers cascading adoption among nearby cities.
- Weak Ties
- The structural insight is robust across substrates: a job-seeker hearing of an opening through an acquaintance, an epidemic crossing between two isolated communities through one rare contact, an idea jumping disciplines through a boundary-spanning researcher, and a few long-range edges making a large graph navigable all exhibit the same topology, as the small-world model of Watts and Strogatz (1998) made formal — a tiny fraction of random long-range rewirings collapses average path length while leaving local clustering nearly intact.
This sourceShows that rewiring a tiny fraction of edges into long-range links collapses average path length while leaving local clustering nearly intact; supports the small-world formalization, the bridge-versus-redundancy complexity compression, the claim that adding a non-redundant link shrinks effective distance faster than strengthening one, and the small-world rewiring example.
Supported in partVerified against the publisher's abstract
The abstract supports the small-world formalization—rewired networks are highly clustered with short path lengths—but not the claim's specific examples or 'tiny fraction' quantitative.
“regular networks ‘rewired’ to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.”
- The structural insight is robust across substrates: a job-seeker hearing of an opening through an acquaintance, an epidemic crossing between two isolated communities through one rare contact, an idea jumping disciplines through a boundary-spanning researcher, and a few long-range edges making a large graph navigable all exhibit the same topology, as the small-world model of Watts and Strogatz (1998) made formal — a tiny fraction of random long-range rewirings collapses average path length while leaving local clustering nearly intact.
Domain-specific¶
Verification¶
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Does it back the claim? Read against the text for 3 of 7 citations: 3 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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Registry ID ref:a853b7b9f39f · see in the full table