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 — bibliography-only; link added.)
- 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.
- 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.
- 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.
- 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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